your first one is not even true.

A=(0,1)

B=(1,2)

C=(2,3)

Your LHS yields

but the RHS is

you should learn a few TeX codes so set theory makes sense.

\cup is union

\cap is intersection

\subset is subset

\supset goes the other way

\in is element of

\emptyset is the nullset

I have no idea what your E is.

Maybe type your question again correctly so we can help?