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[Music]
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thank you
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[Music]
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Hello friends welcome back to our
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channel so in the previous sessions we
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have discussed about the functional
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dependencies and the types of functional
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dependencies and the properties of
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functional dependencies so in this
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session we'll go with the One More
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Concept in dbms that is how to find the
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closure
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of an attribute
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yeah
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so our table will be having a number of
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attributes and will be we have discussed
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about the functional dependencies and
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with the help of those things
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how to find the closure right so because
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this closure is used to identify the
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super keys and the candidate keys right
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so the closure
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of an attribute
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is a set of
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attributes
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set of attributes
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that are
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functionally determined
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where the attribute set
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right so it is a set of attributes so we
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can apply this closure on a single
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attribute
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or
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attribute set
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attribute set that means multiple
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attributes and
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this one disclosure
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is represented
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represented as
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plus the symbol
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as
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C
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if if we want to find X
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the closure of x
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so closure
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X then it is represented as X
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plus X Plus is equal to so set of
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attributes
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the attribute set right so this is the
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closure so which are functionally
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determined by the attribute set
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functionally determined by the
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attribution so we'll see one example so
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that it will be understood
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very clearly
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right so let's have an example
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so let us take this example so let's
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have a relation with the following
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attributes a b c d e and the functional
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dependencies are a tends to b b tends to
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C C tends to D and D tends to a so we
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have discussed about this functional
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dependency concept how it is represented
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and everything so I'll post the link in
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the description section so just go
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through about that so here a tends to b
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means B is a functionally dependent on a
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so by knowing a l we can get the details
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of B
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okay
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so if you want to so from this one we
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can find out the closures different
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closures right so it can be a single
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attribute or a multiple attributes so
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for example if you want to find a plus
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the closure of a plus
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the closure of a plus so
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that means see for every attribute
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for every attribute closure the same
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thing will be determined okay so that
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means C
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if you know a we can get the attribute a
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right so
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for every attribute say
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for which we are finding the closure the
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same attributes will be available in the
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resultant set
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okay same attributes can be included in
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the resultant set so this is the
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resultant set okay so here we are not we
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are supposed to find the closure of EA
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plus so the first one will be the a okay
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by knowing a we can get the details of a
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so for example if if a table consists of
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some employee ID
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and employee number
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or employee name
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employee name so with the help of
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employee ID
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so definitely we can get the details of
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employee ID
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and employee name
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employee ID and employment so similarly
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if you know this one so the self
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attribute can be added into the
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resultant set so
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a plus the first one will be the
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attributes for which we are finding the
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closure right so a and now in the
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resultant set so this is the resultant
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set
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foreign
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what are the other attributes we can
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determine from the functional dependency
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so we are having a so we can move B we
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can get the details of B right so B can
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be determined if you are having a now
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the resultant set is having a and b so
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we are having the details of attributes
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A and B so what are other attributes we
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can get so if you are having attribute B
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we can also get C
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right so the meaning of this functional
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dependency means if you know this
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attribute we can determine this
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attribute
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okay so C is functionally dependent on B
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so we have we know B so obviously we can
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get a c so we can get C now the
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resultant set is having three attributes
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a b c so by knowing A or B or C or a
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combination of a b or V AC or BCE so we
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can get more number of attributes what
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are the other attributes so if you know
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C we can also get a d
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yes
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and
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now the resultant site is having a four
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attributes so again we have to check
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what are the other attributes we can
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determine with the help of all those
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four attributes so we are having D we
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can get a so a is already there so this
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is the closure of a attribute a so for
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example if you want to get the closure
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of B
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d
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so the first one is
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whatever the attributes for which we are
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finding the closure that should be added
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in the resultant set so D will be the
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first one
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okay so if you are having the value of D
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we can get the value of B itself so that
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will be the self okay self instruction
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now in our resultant set we are having
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the value of D from the functional
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dependencies by having the
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what are the other attributes we can get
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so if you know D we can get the
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attributes a we can get the a so a now
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our resultant set is having both d and a
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so
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if you are having a we can get a B
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we can determine the value of B and see
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now the resultant set we are having the
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three d a b so we are having a we can
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get a B so already there we have we are
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having B so we can get the C value
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C
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now the resultant set we are having a
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four attributes a d a b and c so d
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we can get a so already there
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next a we can get a B already there b we
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can get a c already there see we can get
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a d already there so this is a closure
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of t plus
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D Plus and here you can see e now let us
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find the closure of e plus
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e plus
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so the first first
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attribute we can get in the results and
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the resultant set is the self attribute
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so e now the resultant set we are having
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e so from the functional dependencies if
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you know the value of V what are the
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other attributes we can get so there is
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no functional dependency with attribute
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e
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right so you need to find here so there
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is no attribute e so that will be the
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single
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attribute in the resultant set that's a
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single attribute in the resultant set
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and also you can get the details of B
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and C
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so we can get a B and C the closure of
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BC okay BC
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so the first attributes are the self
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attribute so we can get a values of B
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comma C now the resultant sector we are
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having B and C if you know B we can get
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a c already there if you are knowing C
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we can get a d so D and now our
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resultant set we are having a b c d b c
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and d three attributes if you know D U
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we can get a from the functional
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dependencies so EA so this is the
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closure of b c plus
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right so hope you understood so this the
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meaning of this functional dependency
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means if you know the value of a we can
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determine the value of B so that's why
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we call B is a functionally dependent on
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a so here this closure is a set of
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attributes that are functionally
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determined by the attribute set so
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what are the attributes we can determine
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by using this particular attributes is
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the resultant set
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right so hope you understood this one
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this is one example let us move on with
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the second example
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so let us take the second example so
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these are the attributes of a given
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relation r
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and the functional dependencies are this
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one a tends to BC BC tends to d e d
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tends to f and c f comes to G so this
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implies
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if you know a we can get the values of B
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and C so simply you can write it a if
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you know a we can determine B if you
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know a we can determine C
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so we can divide this one and coming to
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this one
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so if you know both the values of B and
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C then only you can determine d e so we
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should not divide the left hand side
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portion that means a determinant
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okay we should not divide the
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determinant so determinant means only
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with the combination of B and C we can
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determine d e
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so this can be decomposed as
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BC
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if you know B and C values we can get a
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d value or if you know B and C values we
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can get a e value
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so you should not divide the
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determinants right so d e can be
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determined only with the help of
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combination of B and C
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okay if you are having only P we can't
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determine D if you are having only C we
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can't determine d
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and similarity DF and this is also same
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CF so with the combination of C and F we
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can determine G so we should not divide
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this one so just remember this one right
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now we find the closures and let us find
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the closure of a plus
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let us find the closure of a plus the
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first one will be yourself
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a so this will be the resultant set
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a resultant set so a now the resultant
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set we are having a so with the help of
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a we are having a so what are the other
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attributes we can determine with the
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help of a from the functional dependency
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so if you are having a we can determine
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either B or C so we can determine either
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b or c
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any other yes right now the resultant
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set we are having a b and c
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in the resultant State we are having a b
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and c now see second functional
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dependency if you are having B and C we
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can determine d e
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so we are having BC okay we have we are
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having B and C so we can determine D or
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e
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so now we are having the results at five
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attributes a b c d e now from this third
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one if you know D we can determine F yes
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yes
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and next one if you know C and F we can
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determine G so in the resultant State we
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are having C and F so we can determine G
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so
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this will be the
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closure of a the closure of a
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and see the next one let us take
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closure of B
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closer of D so here you can observe
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the first one will be the self that is a
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d and now the resultant set we are
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having the value of D so with the help
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of T we can determine the value of e f
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so D comma
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yeah okay D comma yeah now in the
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resultant set we are having D and F both
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the D and F so you can observe here we
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can determine G only with the
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combination of C and F so but in the
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result ends that we are having only F
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there is no C so we can't determine G
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value
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okay so any other attributes which can
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determine with the help of D or F no so
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this will be the
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closure of B plus because here we can
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observe with that with the help of D we
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can determine F and with the help of C
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and F we can determine G
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so only the two things and you can also
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take the
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multiple attributes closure
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see BCD Plus
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that means the closure of b c and d
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the closure of b c and
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so the self that means the First
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characters
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are the B C and D now in our closure in
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our resultant set we are having a b c
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and d so if you know B what are the
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other attributes so from the second
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functional dependency if you know B and
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C we can get a d and e so we are having
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B and C in the resultant cell so we can
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get a d and e already D is available
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here so include e include e now when the
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resultant set we are having b c d e now
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so we if you from the third functional
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dependency if you know D we can get a f
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so we can also get F here and coming to
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the last one so if you know C and F we
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can determine G so here we are having C
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and F we can determine G we can
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determine G so
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any other attributes we can determine so
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we see we can get a d e D we can get F
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see if we can get a g
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right so this is the closure of
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b c d Plus
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right so hope you understood this one
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right so this is the closure this is a
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closure
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we can find from the given functional
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dependency
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right and what is the purpose of finding
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this closure so finding this closure
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will can determine the number of Super
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keys in the number of candidate Keys
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available in the given relation
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right so we can find out what are the
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supercation what are the candidate Keys
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available in the given relation with the
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help of disclosures
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right so uh hope you understood this
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closure let's stop here in the next
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session we'll see more details about the
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closure so what is the purpose that
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means finding the super keys and the
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candid keys from the closures by using
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these closures
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right so let's stop here hope you
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understood this one and if you are
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having any doubts regarding the
16:37
calculation of disclosure so feel free
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to post your thoughts in the comment
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section definitely I will try to clarify
16:42
all your thoughts if you really enjoyed
16:43
my session like my session share my
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thanks for watching thank you very much