Question

Can i please get help with Q 4

Question 4. [3+4+3 = 10 marks] (a) True or false? If you state true, then prove it, otherwise provide a counterexample. Given A, B, C C X, and a function f: X→ X. Then AnB‡Ø ⇒ ƒ(A)n f(BUC) ‡

Answer 1

The statement is false. Here’s a counterexample: Let X = {1, 2, 3}, A = {1}, B = {2}, C = {3}, and f(x) = 1 for all x in X. Then A n B = Ø and f(A) n f(B U C) = {1} n {1} = {1} ≠ Ø.