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

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Home Questions 3AV8ASS2A6

Target Exam

CUET

Subject

Mathematics

Chapter

Sets

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:

The correct answer is Option (1) → $B∩C'$

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,

$(A∪B∪C)∩(A∩B'C')' ∪C'$

$=(B∪C)∩C' = (B∩C')∪(C∩C') = B∩C'$