Even after reviewing my notes over and over again and trying to do these problems over and over again, I still can't figure out how to finish them or start them....

1. Let S, T be sets such that (S \ T) ~ (T \ S). Prove that S ~ T

2. Let S, S1, T, T1 be sets such that S ~ S1 and T ~ T1. Show that S x T ~ S1 X T1

3. Let A, B be subsets of R and nonempty

A is bounded from above and B is bounded from below

Define A - B as the set { z = x - y : x e A, y e B}

Show that sup (A - B) = sup A - inf B

4. Show that [0,1] ~ [0,2)

Hopefully the problems above are understandable...

please help...

- Nicole