Question

in a survey of 100 people, 60 like farming and 65 like civil service. find the number of people who likes farming as well as civil service. also find out how many people like only civil war

Answer 1

Let

• A=set of people like farming
• B=set of people like civil service
• A
  `\cup` B =Total people
• A
  `\cap`B=People like both

We know

`\boxed{\sf n(A\cup B)=n(A)+n(B)-n(A\cap B)}`

`\\ \sf\longmapsto n(A\cap B)=n(A)+n(B)-n(A\cup B)`

`\\ \sf\longmapsto n(A\cap B)=60+65-100`

`\\ \sf\longmapsto n(A\cap B)=125-100`

`\\ \sf\longmapsto n(A\cap B)=25`