If U={1,2,3,4,5,6,7,8,9},A={2,4,6,8} and B={2,3,5,7}. Verify that(i) (A∪B)′=A′∩B′ (ii) (A∩B)′=A′∪B′

U={1,2,3,4,5,6,7,8,9}A={2,4,6,8}B={2,3,5,7}(i) (A∪B)′={2,3,4,5,6,7,8}′={1,9}A′∩B′={1,3,5,7,9}∩{1,4,6,8,9}={1,9}∴(A∪B)′=A′∩B′(ii) (A∩B)′={2}′={1,3,4,5,6,7,8,9}A′∪B′={1,3,5,7,9}∪{1,4,6,8,9}={1,3,4,5,6,7,8,9}∴(A∩B)′=A′∪B′

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

Question

If $U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8}$ and $B = {2, 3, 5, 7} .$ Verify that
(i) $(A \cup B)^{'} = A^{'} \cap B^{'}$ (ii) $(A \cap B)^{'} = A^{'} \cup B^{'}$

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Mila Discussed

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

and

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

Verify that
(i)

(A \cup B)^{'} = A^{'} \cap B^{'}

(ii)

(A \cap B)^{'} = A^{'} \cup B^{'}

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Text solutionVerified

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

A = {2, 4, 6, 8}

B = {2, 3, 5, 7}

(i)

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

A^{'} \cap B^{'} = {1, 3, 5, 7, 9} \cap {1, 4, 6, 8, 9} = {1, 9}

∴ (A \cup B)^{'} = A^{'} \cap B^{'}

(ii)

(A \cap B)^{'} = {2}^{'} = {1, 3, 4, 5, 6, 7, 8, 9}

A^{'} \cup B^{'} = {1, 3, 5, 7, 9} \cup {1, 4, 6, 8, 9} = {1, 3, 4, 5, 6, 7, 8, 9}

∴ (A \cap B)^{'} = A^{'} \cup B^{'}

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Question Text	If $U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8}$ and $B = {2, 3, 5, 7} .$ Verify that (i) $(A \cup B)^{'} = A^{'} \cap B^{'}$ (ii) $(A \cap B)^{'} = A^{'} \cup B^{'}$
Answer Type	Text solution:1
Upvotes	150

If U={1,2,3,4,5,6,7,8,9},A={2,4,6,8} and B={2,3,5,7}. Verify that(i) (A∪B)′=A′∩B′ (ii) (A∩B)′=A′∪B′

Text solutionVerified

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If $U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8}$ and $B = {2, 3, 5, 7} .$ Verify that
(i) $(A \cup B)^{'} = A^{'} \cap B^{'}$ (ii) $(A \cap B)^{'} = A^{'} \cup B^{'}$