Question

Consider the non-empty set consisting of children in a family and a relation $R$ defined as a $Rb$ if $a$ is brother of $b$. Then $R$ is

• A. symmetric but not transitive
• B. transitive but not symmetric
• C. neither symmetric nor transitive
• D. both symmetric and transitive.

Answer 1

The correct option is B transitive but not symmetric

Non empty set containing children in a family aRbaRb a is brother of b

but b need not be brother of a ,can also be sister of a

Therefore it does not imply b R a

R is not symmetric

aRb,bRcaRb,bRc

a is brother of b and b is brother of c

Therefore a must be brother of c

=>aRcaRc

Therefore R is transitive

Relation R is transitive. but not symmetric