Question

If $A\cup B=\{1,2,3,5,6,7,9\},B=\{2,5,7,9\},A\cap B=\{2,5\}$, then represent $A,B$ in Venn-diagrams and verify the relation $n(A\cup B)+n(A\cap B)=n\left(A\right)+n\left(B\right)$.

Answer 1

$a\cup B=\{1,2,3,5,6,7,9\}$

$B=\{2,5,7,9\}$

$A\cap B=\{2,3\}$

$n(A\cup B)+n(A\cup B)=n\left(A\right)+n\left(B\right)$

Now L.H.S

$n(A\cup B)+n(A\cap B)=n(A\cap B)=7+2=9$

R.H.S

$n\left(A\right)+n\left(B\right)=5+4=9$

$L.H.S=R.H.S$