3. Consider the sets:

$$
A=\left\{x \in N^{*} \mid x=k^{2}+k, k<8\right\}, B=\left\{y \in N \mid(y+3) \cdot 2016^{2} \leq 12^{6} \cdot 7^{2}\right\} \text {. }
$$

(4p) a) Determine the elements of the sets $A$ and $B$.

(3p) b) Determine all subsets of two elements of the set $A$, which are also subsets of the set $B$.

Diana Făgețan
3. a) $A=\{2,6,12,20,30,42,56\}$ ..... (1p)
After calculations, we obtain $y \leq 33$ ..... (2p)
$B=\{0,1,2,3,4, . ., 33\}$ ..... (1p)
b) The sought subsets are the 2-element subsets of the set
$A \cap B=\{2,6,12,20,30\}$ ..... (1p)
Thus, $\{2,6\} ;\{2,12\} ;\{2,20\} ;\{2,30\} ;\{6,12\} ;\{6,20\} ;\{6,30\} ;\{12,20\} ;\{12,30\}\{20,30\}$ ..... (2p)