Question

If the set $A$ has $p$ elements, $B$ has $q$ elements then the number of elements in $A\times B$ is

• A. $p+q$
• B. $p+q+1$
• C. $pq$
• D. $p^2$

Answer 1

The correct option is C

$pq$

Explanation for the correct option

Given that,

set $A$ has $p$ elements $\Rightarrow n\left(A\right)=p$

set $B$ has $q$ elements $\Rightarrow n\left(B\right)=q$

We know that number of elements in set $A\times B$is $n\left(A\times B\right)=n\left(A\right)\times n\left(B\right)$

Here, $n\left(A\times B\right)=pq$

Hence, the correct option is option (C) i.e. $pq$.