Question

Let U- {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A={3, 5, 7, 8}, B={2, 3, 8, 9, 10}, and C={1, 4, 7, 8}.


1. (A ∩ B)'
2. A' ∩ B
3. A' ∪ (B ∩ C')
4. A ∩ (B' ∪ C)​

Answer 1

Step-by-step explanation:

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}