Set

If A, B, C are finite sets, and U be the finite universal set, then
i)    n(A U B)=n(A)+n(B) - n(A ∩ B)
ii)    n(A U B)=n(A)+n(B) <=> A,B are disjoint non-void sets.
iii)    n(A-B)= n(A)- n(A ∩ B)
iv)    n(A ∆ B)= Number of elements which belongs to exactly of A or B
        = n(A)+n(B)- 2n(A ∩ B)
v)    n(A U B U C)=n(A)+n(B)+n(C)-n(A ∩ B)-n(B ∩ C)-n(C ∩ A)+ n(A ∩ B ∩ C)
vi)    Number of elements in exactly two of the sets A, B, C
    = n(A ∩ B) + n(B ∩ C) + n(C ∩ A)- 3n(A ∩ B ∩ C)
vii)    Number of elements in exactly one of the sets A, B, C
    = n(A)+n(B)+n(C)- 2n(A ∩ B) - 2n(B ∩ C) - 2n(C ∩ A) + 3n(A ∩ B ∩ C)
viii)    n(A′ U B′)= n((A ∩ B)′)=n(U)-n(A ∩ B)
ix)    n(A′ ∩ B′)= n((A U B)′)=n(U)-n(A U B)