Question

Solve the following problems and verify the data in each case by drawing Venn diagrams.: If $A$ and $B$ are the sets such that $n\left(A\right)=37,n\left(B\right)=26$ and $n(A\cup B)=51,$ find $n(A\cap B)$.

Answer 1

We know that $n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$, where $A$ and $B$ are the respective sets.

Here, it is given that $n\left(A\right)=37,n\left(B\right)=26$ and $n(A\cup B)=51$

Therefore, $n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$

$\Rightarrow 51=37+26-n(A\cap B)$

$\Rightarrow 51=63-n(A\cap B)$

$\Rightarrow n(A\cap B)=63-51$

$\Rightarrow n(A\cap B)=12$

Hence, $n(A\cap B)=12$