Question 22
Let $A$ be a finite set of real numbers. We define the sets
$$
S = \{x + y \mid x, y \in A\}, \quad D = \{x - y \mid x, y \in A\}.
$$
Prove that $\mathrm{card}(A) \cdot \mathrm{card}(D) \leq (\mathrm{card}(S))^2$.
$$
S = \{x + y \mid x, y \in A\}, \quad D = \{x - y \mid x, y \in A\}.
$$
Prove that $\mathrm{card}(A) \cdot \mathrm{card}(D) \leq (\mathrm{card}(S))^2$.