Question

Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9}. A = {2, 4, 6, 8} and B = {2, 3,5,7,8}.
Find (i) A’ (ii) (A’)’ (iii) (A U B)’ (iv)(A ∩ B)’

Answer 1

Given:

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

A = {2, 4, 6, 8} and

B = {2, 3,5,7,8}

To find:

(i) A’ (ii) (A’)’ (iii) (A U B)’ (iv)(A ∩ B)’

Solution:

(i)

A'=Set of elements not in A but in U

A'={1,3,5,7,9}

(ii)

(A')"=Set of elements not in A' but in U

(A')'= {2, 4, 6, 8}

(iii)

AUB=Set of elements in A or in B or in both

AUB={2,3,4,5,6,7,8}

(A U B)’=Set of elements not in AUB but in U

(A U B)’={1,9}

(iv)

A ∩ B = Set of elements common to both A and B

A ∩ B = {2,8}

(A ∩ B)’ = Set of elements not in A ∩ B but in U

(A ∩ B)’ = {1,3,4,5,6,7,9}

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