Question

# If X={1,2,3,4,5,6,7,8,9,10} is the universal set andA={1,2,3,4},B={2,4,6,8},C={3,4,5,6} verify the following.(a) A∪(B∪C)=(A∪B)∪C(b)A∩(B∪C)=(A∩B)∪(A∩C)(c) (A′)′=A

A
Only a is true
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B
Only b and c are true
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C
Only a and b are true
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D
All three a,b and c are true.
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Solution

## The correct option is D All three a,b and c are true.given X={1,2,3,4,5,6,7,8,9,10},A={1,2,3,4},B={2,4,6,8},C={3,4,5,6}now from the given dataA∪B={1,2,3,4,6,8},B∪C={2,3,4,5,6,8}Now A∪(B∪C)={1,2,3,4,5,6,8}and(A∪B)∪C={1,2,3,4,5,6,8} ∴A∪(B∪C)=(A∪B)∪C={1,2,3,4,5,6,8}A∩B={2,4},A∩C={3,4},B∪C={2,3,4,5,6,8}Now A∩(B∪C)={2,3,4}and(A∩B)∪(A∩C)={2,3,4} ∴A∩(B∪C)=(A∩B)∪(A∩C)={2,3,4}A′={5,6,7,8,9,10}therefore (A′)′={1,2,3,4}=Atherefore all three a,b,c are true

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