For any three sets A, B and C the set $(A∪B∪C)∩(A∩B'∩C')'∩C'$ is equal to
Answer & explanation
Correct answer: option 1
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,
$(A∪B∪C)∩(A∩B'∩C')'∪C'$
$=(B∪C)∩C'=(B∩C')∪(C∩C')=(B∩C')$