GATE 2016 question on relation

A binary relation R on N×N is defined as follows: (a,b)R(c,d) if a ≤ c or b ≤ d. Consider the following propositions:

P: R is reflexive

Q: R is transitive

Which one of the following statements is TRUE?

(A) Both P and Q are true

(B) P is true and Q is false.

(C) P is false and Q is true.

(D) Both P and Q are false.

Answer

Things you need to know

refer : http://www.techtud.com/short-notes/basics-relation

Checking for Reflexivity

R is reflexive when (a,b) R (a, b) which is True as a ≤ a or b ≤ b is True.

 

Checking for Transitivity

NOT Transitive as if (a, b) R (c, d) and (c, d) R (p, q) then it is not necessart that (a, b) R (p, q) based on the condition given in the question.

Hence, Ans (B)

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