Question

Let f be a subset of Z × Z defined by f = {(ab, a + b) : a, b ∈ Z}. Is f a function from Z to Z? Justify?

Answer 1

f = {(ab, a + b), a, b ∈ Z}

Let a = 1, b = 1. Then ab = 1, a + b = 2

∴ (1, 2) ∈ f

Let a = – 1, b = – 1. Then, ab = 1, a + b = – 2

∴ (1, – 2) ∈ f

Since, (1, 2) ∈ f and (1, – 2) ∈ f

∴ f is not a function as element 1 does not have a unique image.