[Image of a Function] Let f: XY be a function on set X into set Y....

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[Image of a Function] Let f: X→Y be a function on set X into set Y. Define the image of a set A CX as follows: f(A) = {y Y: 3r A s.t.y = f(x)}. Determine whether the two propositions below are right or not. If the proposition is right, prove it. Give a counterexample otherwise. For any two subsets A and B of X 1. f(An B) = f(A) nf(B); 2. f(AUB) = f(A) U f(B). [Image of a Function] Let f: X→Y be a function on set X into set Y. Define the image of a set A CX as follows: f(A) = {y Y: 3r A s.t.y = f(x)}. Determine whether the two propositions below are right or not. If the proposition is right, prove it. Give a counterexample otherwise. For any two subsets A and B of X 1. f(An B) = f(A) nf(B); 2. f(AUB) = f(A) U f(B).