Question

A and B are subsets of a universal set U in which,n (U)=80, n(A)=50, n(B)=30 and n(A∩B)= 10, the find the value of n(A∪B)

Answer 1

We are given

`\begin{gathered} n(U)=80 \\ n(A)=50 \\ n(B)=30 \\ n(A\cap B)=10 \\ n(A\cup B)?? \end{gathered}`

Note:

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

Solving

`\begin{gathered} n(A\cup B)=n(A)+n(B)-n(A\cap B) \\ n(A\cup B)=50+30-10 \\ n(A\cup B)=70 \end{gathered}`

Therefore,

`n(A\cup B)=70`