Question

For any two sets A and B prove that: n (A-B) = n (A) - n (A intersection B)​

Answer 1

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