1)"Prove $\displaystyle A\cap{A}=A\cup{A}=A$." (This is very first workbook exercise for our Real (and Complex) analysis.)

I have more:2)"Prove that if $\displaystyle a>b\Rightarrow -a<-b$" and prove that3)"square of every negative number is a positive number".

I presume that the more elementary it is, the harder it is (likePrincipiaproving that 1+1=2 (after how many pages?))?

How many ways can such be proven (I think we've done it in discrete math, but workbook is from analysis)?