Question

In a group of $70$ children, $40$ like Vanilla ice-cream $45$ like Chocolate ice-cream. If $25$ children like both Vanilla and Chocolate ice cream, Find out how many like Vanilla ice cream and Chocolate ice cream.

Answer 1

Let $A$ denote children who like Vanilla ice cream, $B$ denote children who like Chocolate ice cream & $U$ denote the universal set of children.

$\Rightarrow$$(\mathrm{A}\cap \mathrm{B})$ will denote children who like both Vanilla and Chocolate ice cream & $(\mathrm{A}\cup \mathrm{B})$ will denote those who like Vanilla or Chocolate ice cream.

So, Given is

$\mathrm{n}\left(\mathrm{A}\right)=40,\mathrm{n}\left(\mathrm{B}\right)=45,\mathrm{n}(\mathrm{A}\cap \mathrm{B})=25\&\mathrm{n}\left(\mathrm{U}\right)=70$

By using relation, $\mathrm{n}(\mathrm{A}\cup \mathrm{B})=\mathrm{n}\left(\mathrm{A}\right)+\mathrm{n}\left(\mathrm{B}\right)-\mathrm{n}(\mathrm{A}\cap \mathrm{B})$ we have

$\mathrm{n}(\mathrm{A}\cup \mathrm{B})=40+45-25$

$\mathrm{n}(\mathrm{A}\cup \mathrm{B})=60$

Hence, there are $60$ children who like Vanilla and Chocolate ice-cream.