[To be turned in on MONDAY (not Friday)]
- Let $\def\P{{\cal P}}\P(A)$ represent the power set of $A$.
- Show that $\P(X-A)-\{\emptyset\}\subseteq\P(X)-\P(A)$ for all sets $X$ and $A$.
- Show that the subset above can not be replaced by an equality.
- Prove by induction: $1+3+5+\cdots+(2n-1) = n^2$ for all natural numbers $n$.
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