Set Theory

[AC369]

Could someone help me with the questions in the screenshots? I don't know if my answers are correct.
Additionally, If A and B are sets and A∪B=A∩B, I know it means A=B. However, would it also imply A and B are proper subsets of each other?

 

[Deleted member 4993]

Could someone help me with the questions in the screenshots? I don't know if my answers are correct.
Additionally, If A and B are sets and A∪B=A∩B, I know it means A=B. However, would it also imply A and B are proper subsets of each other?

Please show us what you have tried and exactly where you are stuck.

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[pka]

If A and B are sets and A∪B=A∩B, I know it means A=B. However, would it also imply A and B are proper subsets of each other?

The answer to that depends upon your definition of proper subset.
In most treatments we read that set \(A\) is a subset of itself but not a proper subset. See here.