Given A = x and B = x ∈ ℤ : 2. Prove A ⊆ B.

Question

Given A = x ∈ ℤ : 4 and B = x. Prove A ⊆ B.

Answer 1

Let a ∈ A. Then a is some integer that is divisible by 4, so we can write a = 4k for some integer k.

We can simultaneously rewrite a as a = 2•2k, so 2 clearly divides a, which means a ∈ B as well.

Therefore A ⊆ B.