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Byju's Answer
Standard XII
Mathematics
Symmetric Relations
If R is a sym...
Question
If R is a symmetric relation on a set A, then write a relation between R and R
−1
.
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Solution
Here, R is symmetric on the set A.
Let
a
,
b
∈
R
⇒
b
,
a
∈
R
Since
R
is
symmetric
⇒
a
,
b
∈
R
-
1
By
definition
of
inverse
relation
⇒
R
⊂
R
-
1
Let
x
,
y
∈
R
-
1
⇒
y
,
x
∈
R
By
definition
of
inverse
relation
⇒
x
,
y
∈
R
Since
R
is
symmetric
⇒
R
-
1
⊂
R
Thus
,
R
=
R
-
1
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