Question

Check whether f: Z × Z → Z × Z (where Z is the set of integers) defined as f(x, y) = (2y, 3x) is injective or not.

Answer 1

Let f(x₁, y₁) = f(x₂, y₂)

(2y₁, 3x₁) = (2y₂, 3x₂)

2y₁ = 2y₂

y₁ = y₂

3x₁ = 3x₂

x₁ = x₂

∴ The function is injective.