Let A and B be two sets. The $(A∪B)'∪(A' ∩ B) =$
Answer & explanation
Correct answer: option 1
We have,
$(A∪B)'∪(A' ∩ B)$
$=(A' ∩ B')∪(A' ∩ B)$
$=(A'∪A')∩(A'∪B)∩(B'∪A')∩(B'∪B)$ [By dist. of ∪ over ∩]
$=A' ∩(A'∪B)∩(B'∪A')∩U$
$=A' ∩(A'∪B)∩(B'∪A')$
$=A' ∩\{(A∩B')'∪(A∩B)\}'$
$=A' ∩\{(A∩B')∩(A∩B)\}'=A'∩A'=A'$