1. Math
  2. Advanced Math
  3. given a function f x y and a...

Question: given a function f x y and a...

Question details

Given a function f : X → Y and a subset A C X, we define the direct image or forward image of A under f to be the set Similarly, if B C Y then we define the preimage or inverse image of B under f to be the set Note that f(X] = im(f). f[A] = {f(x) | x A). Problem 2. Determine whether each statement is true or false. If it is true, prove it. If it is false, prove this by giving a counterexample. (a) For every function f : X → Y and all A. B-X, if An -0, then fA nf[B-0. (b) For every function f : X → Y and all A. B C X. if A nf [B] = 0, then A (c) For every function f : X → Y and all A-X, we have f-1[/A] = A (d) For every function f : X → Y and all A C X, we have f(X \ A] = Y VA (e) For every bijective function f : X → Y and all A, B C X, we have f[An B-fAnf[B].

Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution