Let R be a relation on the set of ordered pairs of positive integers such that ((p, q), (r, s)) ∈ R if and only if p–s = q–r. Which one of the following is true about R?
(A) Both reflexive and symmetric
(B) Reflexive but not symmetric
(C) Not reflexive but symmetric
(D) Neither reflexive nor symmetric
Answer: (C)
Explanation:
((p, q), (r, s)) ∈ R if and only if p–s = q–r (p, q) is not related to (p, q) as p-q is not same as q-p. The relation is symmetric because if p–s = q–r, then s-q = s-p.