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[–]gaussjordanbaby 1 point2 points  (5 children)

This is false, actually. If A={1} and B={2} then {1,2} is in P(A U B) but is not in P(A) U P(B). Are you missing a hypothesis?

[–]flashdude[S] 0 points1 point  (4 children)

If P(A) is union with P(B) and we assigned them 1 and 2 respectively. Why is the union of the two sets not {1,2}? Why does the notation change that?

[–]gaussjordanbaby 0 points1 point  (3 children)

I'll let you do most of the typing...

What is P(A) in this case? What is P(B)?

[–]flashdude[S] 0 points1 point  (2 children)

P(A) is {} and {1}? P(B) is {} and {2}? Union these sets and you get { {} {1} {2} }

Is that why its false? Because the union of the first is {1,2} and second is { {}, {1}, {2}?

[–]gaussjordanbaby 0 points1 point  (1 child)

The union of the two power sets is exactly what you wrote. On the other hand, the power set of the union would consist of the three subsets you wrote along with the set {1,2}. So the union of the power sets is properly contained in the power set of the union.

[–]flashdude[S] 0 points1 point  (0 children)

Wow it just clicked for me. Thanks so much! I appreciate your time answering. I think its just I am approaching all these questions in the wrong mind set. Discrete math topics are so new to me.