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Let f:A->B, where A and B are nonempty, and let T1 and T2 be subsets of B.

a.Prove that f^-1(T1 U T2)= f^-1(T1) U f^-1(T2).
b.Prove that f^-1(T1 intersects T2) = f^-1(T1) intersects f^-1(T2). I think once I see a I can do b.
c. Prove that f^-1(T1) - f^-1(T2) = f^-1(T1-T2).
d. Prove that if T1 is a proper subset of T2, then f^-1(T1) is a proper subset of f^-1(T2).

I am confused on this one and need some help understanding inverse mapping. Thank you

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