যদি A এবং B যে কোন দুইটি সেট হয়, তবে A∩(A∪B) = A∪(A∩B) = কত?

A A∪B

B A∩B

C A

D B

Solution

Correct Answer: Option C

ধরি, A = {1, 2, 3} এবং B = {2, 3, 4}
A∩(AUB)
= {1, 2, 3}∩{1, 2, 3}U{2, 3, 4}
= {1, 2, 3}∩{1, 2, 3, 4) 
= {1, 2, 3}
= A

আবার, AU(A∩B)
= {1, 2, 3}U{1, 2, 3}∩{2, 3, 4}
= {1, 2, 3} U  {2, 3}
= {1, 2, 3} =A
∴  An(AUB)=AU(A∩B) = A

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