Question

# Let A and B be subsets of U with n(U)=100,n(A)=60,n(B′)=30,n(U)=100,n(A)=60,n(B ′ )=30, and n(A U B) = 75, Find n(A ⋂ B)

Equation, expression, and inequalitie
Let A and B be subsets of U with n(U)=100,n(A)=60,n(B′)=30,n(U)=100,n(A)=60,n(B ′ )=30, and n(A U B) = 75, Find $$\displaystyle{n}{\left({A}⋂{B}\right)}$$

Let us recall the formula $$\displaystyle{n}{\left({A}{U}{B}\right)}={n}{\left({A}\right)}+{n}{\left({B}\right)}-{n}{\left({A}⋂{B}\right)}$$
Hence we obtain $$\displaystyle{n}{\left({A}⋂{B}\right)}={n}{\left({A}\right)}+{n}{\left({B}\right)}-{n}{\left({A}{U}{B}\right)}$$ =60+70-75 =55