Question

If $A$ and $B$ are two sets such that $n\left(A\right)=3$ and $n\left(B\right)=5,$ then $n(A\times B)=$ .

• A. $8$
• B. $15$
• C. $10$
• D. $3^5$

Answer 1

The correct option is B $15$

Given two sets $A$ and $B$ are two sets such that $n\left(A\right)=3$ and $n\left(B\right)=5.$
We have $A\times B=\left\{\right(a,b):a\in A,b\in B\}.$
$a$ can take 3 values and $b$ can take 5 values.
$\Rightarrow$ $(a,b)$ can take $3\times 5=15$ values.
i.e., $n(A\times B)=n\left(A\right)\times n\left(B\right)=3\times 5=15$