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)′

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}(i) A′=U−A={5,6,7,8,9}(ii) B′={1,3,5,7,9}(iii) A∪C={1,2,3,4,5,6}∴(A∪C)′={7,8,9}(iv) A∪B={1,2,3,4,6,8}(A∪B)′={5,7,9}(v) We know (A′)′=A⇒ (A′)′={1,2,3,4}(vi) B−C={2,8}∴(B−C)′={1,3,4,5,6,7,9}

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

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) $(A \cup C)^{'}$ (iv) $(A \cup B)^{'}$ (v) $(A^{'})^{'}$ (vi) $(B - C)^{'}$

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Liam Discussed

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 \cup C)^{'}

(iv)

(A \cup B)^{'}

(v)

(A^{'})^{'}

(vi)

(B - C)^{'}

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Text solutionVerified

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}

(i)

A^{'} = U - A = {5, 6, 7, 8, 9}

(ii)

B^{'} = {1, 3, 5, 7, 9}

(iii)

A \cup C = {1, 2, 3, 4, 5, 6}

∴ (A \cup C)^{'} = {7, 8, 9}

(iv)

A \cup B = {1, 2, 3, 4, 6, 8}

(A \cup B)^{'} = {5, 7, 9}

(v) We know

(A^{'})^{'} = A

\Rightarrow (A^{'})^{'} = {1, 2, 3, 4}

(vi)

B - C = {2, 8}

∴ (B - C)^{'} = {1, 3, 4, 5, 6, 7, 9}

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Question Text	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) $(A \cup C)^{'}$ (iv) $(A \cup B)^{'}$ (v) $(A^{'})^{'}$ (vi) $(B - C)^{'}$
Answer Type	Text solution:1
Upvotes	150

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)′

Text solutionVerified

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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) $(A \cup C)^{'}$ (iv) $(A \cup B)^{'}$ (v) $(A^{'})^{'}$ (vi) $(B - C)^{'}$