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  3. proposition 8.59. suppose that x, y, w, z, a, b ar

Proposition 8.59. Suppose that X, Y, W, Z, A, B are sets. Let f : X...

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Advance Math

Proposition 8.59. Suppose that X, Y, W, Z, A, B are sets. Let f: X ? Y , W ? X, Z ? X, A ? Y , and B ? Y . Then the following aretrue:

prove the following ?

(1) f(W ? Z) ? f(W) ? f(Z).


(2) f(W ? Z) = f(W) ? f(Z).


(3) f?1(A ? B) ? f?1(A) ? f?1(B)

4) f?1(A ? B) = f?1(A) ? f?1(B).

(5) X?f?1(A)?f?1(Y ?A).


(6) W ? f?1(f(W)

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