Question

Let U ={1, 2, 3; 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find
(i) $A'$
(ii) $B'$
(iii) $(A ∪ C)'$
**(iv) **$(A ∪ B)'$
**(v) **$(A')'$
(vi) $(B-C)'$

Answer 1

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

(i) $A' =$ {5,6,7,8,9}

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**(ii) **$B' =${1,3,5,7,9}

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(iii) $A\cup C=${1,2,3,4,5,6}
$∴ (A ∪ C)'$ = {7,8,9}

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(iv) $A\cup B=${1,2,3,4,6,8}
$(A ∪ B)'$ = {5,7,9}

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(v) $(A')' = A =$ {1,2,3,4}

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(vi) $B-C =$ {2,8}
$∴ (B-C)' =$ {1,3,4,5,6,7,9}