Question

A and B are two sets given in such a way that $(A\times B)$ contains 6 elements. If three elements of $(A\times B)$ be (1, 3), (2, 5) and (3, 3), find its remaining elements.

Answer 1

Since (1, 3), (2, 5) and (3, 3) are in $(A\times B)$, it follows that 1, 2, 3 are elements of A and 3, 5 are elements of B.

$\therefore (A\times B)=\{1,2,3\}\times \{3,5\}$

$\left\{\right(1,3),(1,5),(2,3),(2,5),(3,3),(3,5\left)\right\}$

Hence, the remaining elements of $(A\times B)$ are (1, 5), (2, 3) and (3, 5)