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Home » Consider the non-empty set consisting of children in a family and a relation R defined as aRb 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
Consider the non-empty set consisting of children in a family and a relation R defined as aRb 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
CBSE | Class 12 | Exercise 1 | Maths | NCERT Exemplar | Relations and Functions
Consider the non-empty set consisting of children in a family and a relation R defined as aRb 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

The correct option is (B) transitive but not symmetric

Given aRb ⇒ a is brother of b.

This does not mean b is also a brother of a as b can be a sister of a.

Therefore, R is not symmetric.

aRb ⇒ a is brother of b.

and bRc ⇒ b is brother of c.

So, a is brother of c.

Thus, R is transitive.

i

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