0:02
[Music]
0:06
thank you
0:09
[Music]
0:12
Hello friends welcome back to our
0:13
channel so in today's session we will
0:15
discuss about one more Topic in a dbms
0:18
that is the properties of a functional
0:20
different dependency
0:27
properties of
0:33
functional dependency
0:39
so actually in the previous session we
0:40
have discussed about this functional
0:42
dependency what exactly this functional
0:44
dependency is and uh
0:47
the anomalies which we have covered in
0:49
the previous session so here we will go
0:51
with the properties of functional
0:52
dependency and these properties are also
0:55
known as
0:56
strong axioms
1:02
and strong axioms
1:05
right so the first property so we know
1:08
that the functional dependency is
1:10
denoted as some extends to Y here x will
1:13
be considered as a determinant and Y is
1:15
it dependent and this we call it as Y is
1:19
functionally dependent on X or X
1:21
determines the Y and we call it as a
1:24
functional dependency if satisfies one
1:27
constraint that consider two random
1:29
pupils so that the x value of both the
1:34
tuples are equal then the Y value of
1:37
corresponding Tuple should also be equal
1:40
so if this constraint is satisfied then
1:42
only we are saying that this is a
1:44
functionally dependent right so this is
1:46
all about our functional dependency now
1:48
the property the first property is
1:50
reflexivity
1:55
reflexivity
1:56
so this reflexity property means if if a
2:02
is set of attributes
2:05
a is a set of attributes
2:08
and B is
2:11
subset of a
2:15
subset of a then
2:18
a tends to B
2:21
is a functionally dependent so this is
2:24
the first property or we can call it as
2:27
a first Armstrong Axiom that is
2:31
the dependent is a subset of determinant
2:35
dependent so this implies that dependent
2:40
is a subset of
2:45
determinant
2:47
determinant so then we call this
2:49
property as a
2:51
reflexivity reflexivity property right
2:55
the second one
2:57
the second one
3:10
so second one is a augmentation
3:13
so this augmentation property so if a
3:17
tends to B
3:19
is a functionally dependent
3:21
then
3:23
if we add some attributes if you add a
3:26
single attribute or a set of attributes
3:29
on both the determined and the dependent
3:32
then also it will be the functionally
3:35
dependent so then
3:39
sorry if C is
3:44
attribute
3:47
all
3:49
set of attributes
3:53
attributes
3:55
added
3:58
to both
4:03
determinant
4:06
and
4:08
dependent
4:11
so simply we can call it as a LHS and
4:14
rhs
4:17
okay lhsn rhs then
4:22
AC tends to CD is also
4:28
functionally dependent it's also
4:31
functionally dependent so adding
4:34
the attributes to both dependent and the
4:37
determinant will also be the
4:40
functionally dependent so this type of
4:43
property or Axiom we call as
4:46
augmentation property or augmentation
4:49
and strong Axiom
4:53
so I hope you understood the first two
4:54
reflexivity and the amps uh this
4:57
augmentation the third one is a
4:59
transitivity
5:02
the third one is a try transivity
5:07
see
5:08
third one
5:11
transitivity
5:14
so if a tends to B
5:19
is functionally dependent
5:22
and
5:23
B tends to C is also functionally
5:27
dependent
5:29
then the transitivity rule says that a
5:33
tends to C
5:35
is also functionally dependent so this
5:39
is called transitivity Rule right if a
5:43
tends to B is a functionally dependent
5:45
and B tends to C is also functionally
5:47
dependent that implies we can get b if
5:51
you know a and if you get C if you know
5:54
B so obviously you can get a c if you
5:57
know a so that is called the
6:00
transitivity Axiom or transitivity
6:03
property so the three Armstrong axioms
6:07
of functional dependencies are
6:11
one is
6:15
so one is a reflexivity
6:24
another one is augmentation
6:29
the next one is
6:35
transitivity
6:37
so these three are the amstrong axioms
6:39
and apart from these amps from axioms we
6:42
are also having some rules inference
6:44
rules right so which are derived from
6:47
these
6:48
and strong axioms so let us check this
6:52
this inference rules which are derived
6:55
from the Armstrong axioms
7:02
so
7:04
inference
7:06
rules
7:08
and also we can call it as a secondary
7:11
rules
7:13
secondary rules so these are derived
7:17
from
7:19
foreign
7:24
axioms okay the these are derived from
7:27
the Armstrong axioms the first rule
7:31
is a union
7:33
so
7:36
if a tends to B is a functionally
7:40
dependent
7:42
and a tends to C is also a functionally
7:46
dependent
7:47
then
7:49
a tends to BC is also
7:54
functionally dependent so this type of
7:57
rule we call it as a union so if a tends
8:01
to be a tends to C simply we can combine
8:04
this if you know a we can get b if you
8:06
know a we can get C so if you know a we
8:09
can get a B and C so you no need to
8:11
write a two dependencies right so we can
8:13
combine that so this type of property we
8:16
call it as a union union property or
8:18
Union rule
8:19
the next one
8:25
second one
8:30
composition
8:33
so what is this a composition right so
8:36
if a tends to be
8:39
is functionally dependency
8:41
and C tends to D is also a functionally
8:45
dependent C then
8:48
combining both the dependence and
8:50
combining both the determinants so AC
8:53
tends to b d is also
8:58
functionally dependent right so
9:01
combining both the determinants and both
9:04
the dependents if you know A and C we
9:06
can get the values B and T right so this
9:10
type of thing we call it as a
9:11
composition
9:13
this type of property or uh rules we
9:16
call it as a composition
9:19
right hope you understood this one next
9:22
the third one is a decomposition
9:34
decomposition so what is this
9:36
decomposition so if
9:41
a tends to B and C
9:44
okay that means
9:46
is an functional dependent
9:49
so if you know J we can get B and C so
9:51
this can be divided
9:54
this can be divided
9:56
a tends to b and a tends to C
10:02
so both are
10:04
functionally dependents so this is
10:07
called a decomposition that means a
10:09
dividing dividing the functional
10:10
dependency so we are dividing this
10:13
functional dependency so a tends to B is
10:15
a functionality dependent and a tends to
10:17
C is also a functionally dependent so
10:20
such type of rule we call it as a
10:22
decomposition decomposition
10:26
and the next one the last one is in
10:28
pseudo trans
10:44
itivity so here the transitivity rule we
10:47
have seen in the previous just now that
10:49
is if a tends to B and B tends to C
10:54
so simply we can say a tends to C so
10:57
this is a transitive so here the pseudo
11:00
Transit it says if a tends to be
11:05
and BC tends to D so is an a
11:09
functionally dependent and is here also
11:12
it is a functionally dependent so then
11:14
then we can say that AC tends to D
11:21
is also functionally dependent which is
11:24
similar to our transitivity rule which
11:26
is similar to our transitivity rule so
11:29
this called as a pseudo transitivity so
11:32
if a tends to B is an functionally
11:34
dependent and a b c tends to B is a
11:36
functionally dependent so simply a c
11:39
tends to B will also be the functionally
11:41
dependent
11:42
so this type of thing we call it as a
11:44
pseudotransit rate so there there are
11:47
four rules called as a inference rules
11:50
or we can call them as a secondary roots
11:54
so
11:55
the first one
11:58
Union
12:02
composition
12:07
decomposition
12:15
pseudotransitivity
12:19
so these four are the inference rules
12:22
which are derived from the axioms which
12:25
are derived from the axioms right so
12:28
hope you understood these properties of
12:30
functional dependencies and also we call
12:32
it as amstrong axioms right so if you
12:35
are having any uh doubts regarding this
12:37
session feel free to post your doubts in
12:39
the comment section I definitely I'll
12:41
try to clarify all your doubts and if
12:43
you really enjoyed my session like my
12:45
session share my session with your
12:46
friends and don't forget to subscribe to
12:48
our Channel thanks for watching thank
12:50
you very much