Question

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

C = { 3, 4, 5, 6 }. Find (i) A′ (ii) B′ (iii) (A UC)′

(iv) (A U B)′ (v) (A′)′ (vi) (B – C)′

very urgent ​

Answer 1

$\sf{\huge{\underline{\purple{Given :-}}}}$

• U = {1, 2, 3, 4, 5, 6,7,8,9}

• A = {1,2, 3,4}

• B = {2, 4, 6,8}

• C = { 3, 4, 5, 6 }

$\sf{\huge{\underline{\pink{To\:Find :-}}}}$

• A′

• B′

• (A U C )′

• (A U B)′

• (A′)′

• (B – C)′

$\sf{\huge{\underline{\blue{Solution :-}}}}$

We have, A universal set, U = {1, 2, 3, 4, 5, 6,7,8,9}

• Á

➝ Á = U - A

➝ {1, 2, 3, 4, 5, 6,7,8,9} - {1,2, 3,4}

➝ {5, 6 ,7 , 8, 9}

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• B′

➝ B' = U - B

➝ {1, 2, 3, 4, 5, 6,7,8,9} - {2, 4, 6,8}

➝ {1, 3, 5, 7 ,9}

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• (A U C)′

➝ AUC = {1,2, 3,4} U { 3, 4, 5, 6 }

➝ { 1 , 2 , 3 , 4 , 5 , 6 }

(A U C)′ = U - AUC

➝ {1, 2, 3, 4, 5, 6, 7 ,8 ,9} - { 1 , 2 , 3 , 4 , 5 , 6 }

➝ { 7 ,8 ,9 }

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• (A U B)′

➝ A' ∩ B'

➝ {5, 6 ,7 , 8, 9} ∩ {1, 3, 5, 7 ,9}

➝ {5, 7 , 9}

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• (A′)′

➝ (A′)′ = A

➝ {1,2, 3,4}

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• (B – C)′

➝ (B - C ) = B - ( B ∩ C )

( B ∩ C ) = {2, 4, 6,8} ∩ { 3, 4, 5, 6 }

➝ {2, 4, 6,8} - { 4, 6 }

➝ {2, 8}

(B – C)′ = U - ( B - C )

➝ {1, 2, 3, 4, 5, 6 , 7, 8, 9} - { 2, 8 }

➝ {1, 3, 4, 5, 6 , 7, 9}

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