Question

If $\left(1,3\right),\left(2,5\right)$ are $\left(3,3\right)$ three elements of $\left(A\times B\right)$ and the total number of elements in $\left(A\times B\right)$ is $6$, then the remaining elements of $A\times B$ are

• A. $(1,5);(2,3);(3,5)$
• B. $(5,1);(3,2);(5,3)$
• C. $(1,5);(2,3);(5,3)$
• D. none of these

Answer 1

The correct option is A

$(1,5);(2,3);(3,5)$

Explanation for correct option:

Given, $\left(A\times B\right)=6$ and $\left(A\times B\right)=\left\{\left(1,3\right),\left(2,5\right),\left(3,3\right)\right\}$

We know that Cartesian product of set $A=\left\{a,b\right\}\&B=\left\{c,d\right\}$ is $A\times B=\left\{\left(a,c\right),\left(a,d\right),\left(b,c\right),\left(b,d\right)\right\}$

Therefore, $A=\left\{1,2,3\right\}\&B=\left\{3,5\right\}$

$\Rightarrow$$A\times B=\left\{\left(1,3\right),\left(1,5\right),\left(2,3\right),\left(2,5\right),\left(3,3\right),\left(3,5\right)\right\}$

Thus, remaining elements are $A\times B=\left\{\left(1,5\right),\left(2,3\right),\left(3,5\right)\right\}$

Hence, correct answer is option $\left(A\right)$.