Q. 295.0( 1 Vote )
Consider the non- A. symmetric but not transitive
B. transitive but not symmetric
C. neither symmetric nor transitive
D. both symmetric and transitive
Given that, relation R is defined as aRb if a is brother of b
aRa ⇒ a is brother of a, which is not true.
⇒ (a,a) ∉ R
⇒ R is not reflexive
aRb ⇒ a is brother of b but this does not mean that b is brother of a,b can be sister of a.
Thus, (a,b) ∈ R ⇒ (b,a) ∉ R
⇒ R is not symmetric.
aRb ⇒ a is brother of b and bRc ⇒ b is brother of c
⇒ a is a brother of c.
⇒ R is transitive.
Hence, R is transitive but not symmetric.
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