Question

Let A and B be two sets having 3 and 6 elements respectively. Write the minimum number of elements that $A\cup B$ can have.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{know}\mathrm{that}n\left(A\cup B\right)=n\left(A\right)+n\left(B\right)-n\left(A\cap B\right) \\ n\left(A\cup B\right)\mathrm{is}\mathrm{minimum}\mathrm{when}n\left(A\cap B\right)\mathrm{is}\mathrm{maximum} \\ \mathrm{so},n\left(A\cap B\right)=3 \\ \mathrm{Hence},n\left(A\cup B\right)=n\left(A\right)+n\left(B\right)-n\left(A\cap B\right) \\ =3+6-3 \\ =6 \end{gathered}$$