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I've been working on this homework problem for a while now and I can't seem to figure it out.

The problem is as follows:

Prove that for any sets $A$ and $B$, $P(A) \cup P(B) = P(A\cup B)$ then either $A\subseteq B$ or $B\subseteq A$. I'm having trouble understanding what it means to have an equation as one of my hypotheses.

I looked online and I couldn't find anything online, so hopefully this is alright.

Thanks!

Any help would be appreciated

Asaf Karagila
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mrmathboi
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  • Equation as hypothesis: for any real number $x$, if $x^2 = 2$ then either $x = \sqrt{2}$ or $x = -\sqrt{2}$. – Patrick Stevens Feb 28 '18 at 22:45
  • Probably easiest to prove by contraposition. If neither $A \subseteq B$ or $B \subseteq A$, then there are $x \in A, y \in B$ such that $x \notin B$ and $y \notin A$. Now consider the set ${x,y}$. – Hans Engler Feb 28 '18 at 22:48
  • https://math.stackexchange.com/questions/246491/stuck-with-proof-for-forall-a-forall-b-mathcalpa-cup-mathcalpb-mathc – Lucas Feb 28 '18 at 22:55

0 Answers0