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GATE 2015 CS (CS3) – Question 60

Engineering Mathematics · Discrete Mathematics: Sets, Relations, Functions, Partial Orders and Lattices · 2 marks · Multiple choice

On ordered pairs of positive integers, ((p,q),(r,s))∈R iff p−s=q−r. Which describes R?

  1. Reflexive and symmetric
  2. Reflexive but not symmetric
  3. Not reflexive but symmetric
  4. Neither reflexive nor symmetric

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Correct answer: (C) Not reflexive but symmetric

Explanation

The relation is equivalently p+r=q+s, unchanged when the two ordered pairs are swapped, so it is symmetric. Relating (p,q) to itself would require 2p=2q, which fails for a general pair such as (1,2). Hence it is not reflexive. Answer C.

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