Let U 12315 be a universal set with subsets E 2468 F I 3

Let U = {1,2,3,...,15} be a universal set with subsets E = {2,4,6,8}, F = {I, 3, 5,7, 9}, and G = {7, 8, 9, 10, 11, 12}. What is n((E U F)\' n G\') ?

Solution

Taking E U F first,

E U F = {1,2,3,4,5,6,7,8,9}

Taking its complement,

(E U F)\' = {10, 11, 12, 13, 14, 15}

Now, taking the complement of G,

G\' = {1,2,3,4,5,6,13,14,15}

Thus,

(E U F)\' intersection G = {13,14,15}

Hence, as there are 3 elements here,

n((E U F)\' intersection G) = 3 [ANSWER]