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Determine whether each statement is true or false. If it is true, prove it. If it...

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Advance Math

Determine whether each statement is true or false. If it istrue, prove it. If it is false, give a counterexample.

a) For every function f : X ? Y and all A ? X, we have f^?1[f[A]] = A.

(b) For every function f : X ? Y and all A ? X, we have f[X A]= Y f[A].

(c) For every function f : X ? Y and all A, B ? Y , we have f^?1[A ? B] = f^?1 [A] ? f^?1 [B].

(d) For every function f : X ? Y and all A, B ? X, we have f[A ?B] = f[A] ? f[B].

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