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RELATIONS AND FUNCTIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRELATIONS AND FUNCTIONS1 Mark
Question
Choose the correct answer from the given four options.
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:
  1. Symmetric but not transitive.
  2. Transitive but not symmetric.
  3. Neither symmetric nor transitive.
  4. Both symmetric and transitive.
✓

Answer

  1. Transitive but not symmetric.

Solution:

We are given that a relation R defined aRb ⇒ a is brother of b.

aRa ⇒ a is brother of a, which is not true.

Hence, R is not reflexive.

aRb ⇒ a is brother of b.

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

Hence, it is not symmetric.

aRb ⇒ a is brother of b

and bRc ⇒ b is a brother of c.

So, a is brother of c.

Hence, R is transitive.

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