Solution
We are given
[tex]\begin{gathered} n(U)=80 \\ n(A)=50 \\ n(B)=30 \\ n(A\cap B)=10 \\ n(A\cup B)?? \end{gathered}[/tex]Note:
[tex]n(A\cup B)=n(A)+n(B)-n(A\cap B)[/tex]Solving
[tex]\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}[/tex]Therefore,
[tex]n(A\cup B)=70[/tex]