Question

Let S = { 1 , 2 , 3 , ... , 18 , 19 , 20 }

S = { 1 , 2 , 3 , ... , 18 , 19 , 20 } be the universal set. Let sets A and B be subsets of S , where: Set A = { 4 , 6 , 10 , 11 , 12 , 15 , 16 , 18 , 19 , 20 }

Set B = { 1 , 3 , 5 , 7 , 8 , 9 , 12 , 13 , 14 , 16 , 17 , 18 , 20 }

Determine the following:

n ( A ) =

n ( ¯¯¯ A ) =

n ( B ) =

n ( A ∩ B ) =

n ( A ∪ B ) =

Answer 1

A = {4, 6, 10, 11, 12, 15, 16, 18, 19, 20}

Since the number of elements in set A is 4, so

n(A) = 10

= {1, 2, 3, 5, 7, 8, 9, 13, 14, 17}

Since no of elements in set is 10, so

n() = 10

B = {1, 3, 5, 7, 8, 9, 12, 13, 14, 16, 17, 18, 20}

Since the no of elements in set B is 13, so

n(B) = 13

(A B) = { 12, 16, 18, 20}

Since no of elements in set (A B) is 4, so

n(A B) = 4

(A U B) = {1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

Since no of elements in set (A U B) is 19,so

n(A U B) = 19