# Math Help - 30 minute set theory

1. ## 30 minute set theory

1. if X is a set, find $X\cap P(X)$

I think it's $X$ but I don't know how to show it

2. if $P(X) = P(Y)$, is necessarily $X + Y$ justify your answer

2. $X = \left\{ {a,b} \right\}\,\& \,P(X) = \left\{ {\emptyset ,\{ a\} ,\{ b\} ,\{ a,b\} } \right\}$
Is there a single element in both of those sets?

As for #2. I have no idea what $X+Y$ could mean.
In the last century older mathematicians such as R L Moore used it to mean union. Is that the case here?

3. oops I just held the shift button
it's X = Y

4. Originally Posted by jbpellerin
it's X = Y
$t \in X \Rightarrow \left\{ t \right\} \in P(X) = P(Y) \Rightarrow t \in Y \Rightarrow X \subseteq Y$
Now you finish it.