Question

Let $A$ and $B$ be two sets such that $A\times B$ Consists of $6$ elements. If three elements of $A\times B$ are $(1,4),(2,6),(3,6)$ then $B\times A$. is $=\{(a,1),(6,1),(4,d),(c,2),(4,3)(b,3)\}$. Find $a+b+c+d$

Answer 1

From the given ordered pairs of $A\times B$ we conclude that $A=\{1,2,3\},B=\{4,6\}$

Since $A\times B$ has six elements i.e. $3\times 2$, $A$ and $B$ are as stated above.

$\therefore A\times B=\{(1,4),(1,6),(2,4),(2,6),(3,4),(3,6)\}$

By reversing the above ordered pairs, we get

$B\times A=\{(4,1),(6,1),(4,2),(6,2),(4,3)(6,3)\}.$
$\Rightarrow a+b+c+d=18$