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

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

Expert Solution

Colby Messinger answered 2 years ago

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