Answer
See the detail below
Work Step by Step
A = {m ∈ Z | m = 2a for some integer a} and B = {n ∈ Z | n = 2b – 2 for some integer b}
To prove that B is a subset of A, we need to show that every element in B is also an element of A.
Let's take an element x ∈ B. By definition, x is an integer that satisfies the equation x = 2b - 2 for some integer b.
To prove that x ∈ A, we need to show that x can be expressed in the form x = 2a for some integer a.
Starting with the equation x = 2b - 2, we can rewrite it as x = 2(b - 1)
Let's define a new integer c = b - 1. Now we have x = 2c
Since c is an integer (since b is an integer), we have expressed x in the form x = 2a, where a = c.
Therefore, for any element x ∈ B, we have shown that x ∈ A.
Thus, we have proved that B ⊆ A.
