IF X = 1, SINCE 1 ∈ Z+ AND 12 < 10, THEN X ∈ B

23. Let x ∈ A. Then x = 1, 2, 3. If x = 1, since 1 ∈ Z

⁺

and 1

²

< 10, then x ∈ B. If x = 2, since

2 ∈ Z

⁺

and 2

²

< 10, then x ∈ B. If x = 3, since 3 ∈ Z

⁺

and 3

²

< 10, then x ∈ B. Thus if

x ∈ A, then x ∈ B .

Now suppose that x ∈ B. Then x ∈ Z

⁺

and x

²

< 10. If x ≥ 4, then x

²

> 10 and, for these

values of x, x / ∈ B. Therefore x = 1, 2, 3. For each of these values, x

²

< 10 and x is indeed in

B. Also, for each of the values x = 1, 2, 3, x ∈ A. Thus if x ∈ B, then x ∈ A. Therefore A = B.