Question

From the given Venn diagram find
(i) $A$
(ii) $B$
(iii) $A\cup B$
(iv) $A\cap B$
Also verify that $n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$

Answer 1

From the Venn diagram
(i) $A=\{a,b,d,e,g,h\}$
(ii) $B=\{b,c,e,f,h,i,j\}$
(iii) $A\cup B=\{a,b,c,d,e,f,g,h,i,j\}$ and
(iv) $A\cap B=\{b,e,h\}$
So, $n\left(A\right)=6,n\left(B\right)=7,n(A\cup B)=10,n(A\cap B)=3$. Now
$n\left(A\right)+n\left(B\right)-n(A\cap B)=6+7-3=10$
Hence, $n\left(A\right)+n\left(B\right)-n(A\cap B)=n(A\cup B)$