For any three sets A, B and C the set $(

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

For any three sets A, B and C the set $(A∪B∪C)∩(A∩B'∩C')'∩C'$ is equal to

Options:

$B∩C'$

$B'∩C'$

$B∩C$

$A∩B∩C$

Correct Answer:

$B∩C'$

Explanation:

We have,

$(A∩B'∩C')'=A'∪B∪C$

$∴(A∪B∪C)∩(A∩B'∩C')'$

$=(A∪B∪C)∩(A'∪B∪C)$

$=(A∩A')∪(B∪C)$ [By distributivity of ∪ over ∩]

$=\phi∪(B∪C)=B∪C$

Hence,

$(A∪B∪C)∩(A∩B'∩C')'∪C'$

$=(B∪C)∩C'=(B∩C')∪(C∩C')=(B∩C')$