If R = {(x,y) : x,y are integers such that x - y is divisible by 5} sh – InterviewSolution

1.

If R = {(x,y) : x,y are integers such that x - y is divisible by 5} show that R is reflexive and symmetric.

Answer»

Let x,y,z ∈ z, then

(i) x - x is divisible by 5 ∀ x ∈ z

∴ R is reflexive

(ii) If x - y is divisible by 5, then y - x is also divisible by 5 ∀ x, y ∈ z ∀ x, y ∈ z

∴ R is symmetric

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