Let A and B be two sets. The $(A∪B)'

CUET Preparation Today

Start Free Mocks

Home Questions PDNMAZXH8T

Target Exam

CUET

Subject

Mathematics

Chapter

Sets

Question:

Let A and B be two sets. The $(A∪B)'∪(A' ∩ B) =$

Options:

$A'$

$B'$

none of these

Correct Answer:

$A'$

Explanation:

We have,

$(A∪B)'∪(A' ∩ B)$

$=(A' ∩ B')∪(A' ∩ B)$

$=(A'∪A')∩(A'∪B)∩(B'∪A')∩(B'∪B)$ [By dist. of ∪ over ∩]

$=A' ∩(A'∪B)∩(B'∪A')∩U$

$=A' ∩(A'∪B)∩(B'∪A')$

$=A' ∩\{(A∩B')'∪(A∩B)\}'$

$=A' ∩\{(A∩B')∩(A∩B)\}'=A'∩A'=A'$