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

Similar Questions

Start a Free Trial Now

Confusing about what to choose? Our team will schedule a demo shortly.