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Byju's Answer
Standard XII
Mathematics
Domain
Relation R in...
Question
Relation R in the set A of human beings in a town at a particular time given by
R
=
{
(
x
,
y
)
:
x
a
n
d
y
l
i
v
e
i
n
t
h
e
s
a
m
e
l
o
c
a
l
i
t
y
}
enter 1-reflexive and transitive but not symmetric
2-reflexive only
3-Transitive only
4-Equivalence
5-None
Open in App
Solution
R
=
{
(
x
,
y
)
:
x and y live in the same locality
}
Clearly
(
x
,
y
)
∈
R
as
x
and
x
is the same human being.
∴
R
is reflexive.
If
(
x
,
y
)
∈
R
, then
x
and
y
live in the same locality.
⇒
y
and
x
live in the same locality.
⇒
(
y
,
x
)
∈
R
∴
R
is symmetric.
Now, let
(
x
,
y
)
∈
R
and
(
y
,
z
)
∈
R
.
⇒
x
and
y
live in the same locality and
y
and
z
live in the same locality.
⇒
x
and
z
live in the same locality.
⇒
(
x
,
z
)
∈
R
∴
R
is transitive.
Hence,
R
is reflexive, symmetric and transitive.
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0
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Q.
Relation R in the set A of human beings in a town at a particular time given by
R
=
{
(
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Q.
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x
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Q.
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3-Transitive only
4-Equivalence
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