here is my question. Please help.

[Q1] (3 X 5 = 15 points) Consider the NVS with R as the mother set and the Euclidean norm. (a) Prove that (-1, 1) is a convex subset. (b) Prove that (-1, 0) U(0, 1) is not a convex subset. (c) Prove that [a, b] is compact subset, where a, be R. (d) Provide an example of a subset that is not compact. Prove it. (e) Draw a function function from (R, ne) to (R, ne) that is discontinuous at some input To. Pro- vide a stepwise explanation of why the function is discontinuous at To