I need help determining if these are true or false and then finding a counterexample if they are false.

6. [60 pts) Tore or False {if falSE, give a counterexample). a {10 pts) Let f : (X, J} > (Y, J\") be continuous. If A is a connected subset of Y, then f'1(A) is a connected subset of X. b {10 pts} Let f : (X, J] > (Y, J\") be continuous. [f A is a compact subset of Y, then f'1(A) is a compact subset of X. c [10 pts) If A and B are two compact subsets of X, then AU B is also a compact subset of X. (1 [10 pts) If A is s compact subset of X and B is a closed subset of X, then A F] B is a. closed subset of X. e {10 pts} If A and B are two subsets of X such that A g B, then A Q B. f (10 pts] Let f : {0, 1} + [(1,1) be continuous. Then there is s z E (O, 1) such that z) = z