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1.Relation and Function
normal
If $R$ is an equivalence relation on a set $A$, then ${R^{ - 1}}$ is
A
Reflexive only
B
Symmetric but not transitive
C
Equivalence
D
None of these
Solution
Consider $A=\{a, b, c\}$
$R:\{(a, a\},(b, b),(c, c),(a, b),(b, a),(a, c),(c, a),(b, c),(c, a)\}$
$R ^{-1}=\{( a , a \},( b , b ),( c , c ),( b , a ),( a , b ),( c , a ),( a , c ),( c , b ),( a , c )\}$
$R ^{-1}$ is reflexive, symmetric and transitive.
So, $R ^{-1}$ is an equivalence relation.
Standard 12
Mathematics