1) Let A, B be subsets of R^n that are pathwise connected with A interset B not empty. Prove A U B is pathwise connected.

2) Prove S = {(x,y) in R^2 : either x or y is rational number} is pathwise connected.

I have been studying for two weeks, and will continue to study tonight, but I simply cannot study some problems that I do not have the answers for.

Thank you!