Find the number of elements in A1 Union A2 Union A3 if there

Find the number of elements in A_1 Union A_2 Union A_3 if there are 98 elements in A_1, 1001 elements in A_2, and 9975 elements in A_3 in each of the following situations: The sets are pairwise disjoint. There are 17 elements common to each pair of sets and 5 elements in all three sets.

Solution

Given there are three sets named A1,A2,A3.

A1 has 98 elements

A2 has 1001 elements

A3 has 9975 elements.

a)Need to find the number of elements in (A1UA2UA3) when the 3 sets are pairwise disjoint.

Let \'n\' represents number of elements.

n(A1UA2UA3) = n(A1)+n(A2)+n(A3)

= 98+1001+9975

= 11,074

Therefore, number of elements in A1UA2UA3 = 11,074

b)Need to find the enumber of elements in (A1UA2UA3) when there are 17 elements are common to each pair of sets and 5 elements are in all 3 sets.

n(A1UA2UA3) = n(A1)+n(A2)+n(A3)-n(A1nA2)-n(A2nA3)-n(A3nA1)+n(A1nA2nA3)

= 98+1001+9975-17-17-17+5

= 11,028

Therefore, number of elements in A1UA2UA3 = 11,028