Question

Prove
n(A-B) = n(A) - n(A ∩B) ?

Answer 1

Step-by-step explanation:

For every element x∈Ax∈A we have either x∈A∩Bx∈A∩B or x∈A−Bx∈A−B, but never both. Thus, the number of elements in AA is equal to the number of elements in A∩BA∩B plus the number of elements in A−BA−B, i.e. n(A)=n(A∩B)+n(A−B)n(A)=n(A∩B)+n(A−B).