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

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

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

Printable View

- Sep 24th 2008, 11:01 AMjbpellerin30 minute set theory
1. if X is a set, find $\displaystyle X\cap P(X)$

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

2. if $\displaystyle P(X) = P(Y)$, is necessarily $\displaystyle X + Y$ justify your answer - Sep 24th 2008, 11:26 AMPlato
$\displaystyle X = \left\{ {a,b} \right\}\,\& \,P(X) = \left\{ {\emptyset ,\{ a\} ,\{ b\} ,\{ a,b\} } \right\}$

Is there a single element in both of those sets?

As for #2. I have no idea what $\displaystyle X+Y$ could mean.

In the last century older mathematicians such as R L Moore used it to mean union. Is that the case here? - Sep 24th 2008, 11:31 AMjbpellerin
oops I just held the shift button

it's X = Y - Sep 24th 2008, 11:42 AMPlato