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GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 1

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If $A$ and $B$ are two sets and $A \cup B = A \cap B$ then

  1. $A=\phi$
  2. $B=\phi$
  3. $A\neq B$
  4. $A=B$
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1 Answer

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Answer is D

Option A : Lets say B = {1} and A=ϕ (given) then ϕUB = BՈϕ => Bǂϕ 
Option B : Lets say A = {1} and B=ϕ (given) then AUϕ = ϕՈA => Aǂϕ
Option C : Lets say A = {1,2,3} and B={1,2} then AUB = BՈA => {1,2,3} ǂ {1,2} 
Option D :      AUB = BՈA 
                  => AUA = AՈA   (since, A=B)
                  => A=A

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