Let A={0,1,2,3,4,5}, B={3,4,5,6,7}, C={6,7,8,9}. Find:
i. A ∪ B
ii. B ∩ C
iii. A ∩ C
iv. A U (B ∩ C)
Answers
Answer:
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)
′
Solution
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}
Step-by-step explanation:
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)
′
Medium
Solution
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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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