Question

Let A and B be two sets having 4 and 7 elements respectively. Then write the maximum number of elements that $A\cup B$ can have.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{know}\mathrm{that}n\left(A\cup B\right)=n\left(A\right)+n\left(B\right)-n\left(A\cap B\right) \\ n\left(A\cup B\right)\mathrm{is}\mathrm{maximum}\mathrm{when}n\left(A\cap B\right)\mathrm{is}\mathrm{minimum} \\ \mathrm{so},n\left(A\cap B\right)=0 \\ \mathrm{Hence},n\left(A\cup B\right)=n\left(A\right)+n\left(B\right)-n\left(A\cap B\right) \\ =4+7-0 \\ =11 \end{gathered}$$