If A = {x ∈ ℤ : −7 ≤ x ≤ 7}, B = {x ∈ ℤ : x² ≤ 16}, and C = {x ∈ ℤ : 3 divides x}, what is (A − B) ∩ C?

{−6, 6}

Since x² ≤ 16, the integer x must lie between −4 and 4, so B = {−4, −3, −2, −1, 0, 1, 2, 3, 4}. Therefore, removing B from A = {−7, …, 7} leaves A − B = {−7, −6, −5, 5, 6, 7}. Among these remaining elements, only −6 and 6 are divisible by 3. Hence (A − B) ∩ C = {−6, 6}, which is option A.

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).