List of Formulae

1. $n(A∪B)=n(A)+n(B)−n(A∩B)$
2. $n(A')=n(U)−n(A)$
3. $n(A−B)=n(A)−n(A∩B)$
4. $n((A∪B)’)=n(A’∩B’)$
5. $n((A∩B)’)=n(A’∪B’)$
6. $n(A’∩B’)=n(U)−n(A∪B)$
7. $n(A’∪B’)=n(U)−n(A∩B)$

Practice Questions:

1. If X and Y are two sets such that X ∪ Y has 50 elements, X has 28 elements and Y has 32 elements, how many elements does X ∩ Y have ?
2. In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach both physics and mathematics. How many teach physics ?
3. If X and Y are two sets such that n ( X ) = 17, n ( Y ) = 23 and n ( X ∪ Y ) = 38, find n ( X ∩ Y ).
4. If X and Y are two sets such that X ∪ Y has 18 elements, X has 8 elements and Y has 15 elements ; how many elements does X ∩ Y have?
5. If X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and X ∩ Y has 10 elements, how many elements does Y have?
6. If S and T are two sets such that S has 21 elements, T has 32 elements, and S ∩ T has 11 elements, how many elements does S ∪ T have?