Decide which of the following statements are true and which are false. Prove the true ones and give counterexamples to the false ones.
a) Let f(x) = sin x. Then the function

is a bijection, and its inverse function is arcsin x.
b) Suppose that A, B, and C are subsets of some set X and that f : X †’ X. If A ˆ© B ‰  θ.
c) Suppose that A and B are subsets of some set X. Then (AB)C = BA.
d) If f takes [-1,1] onto [-1,1], then f-1 (f({0})) = {0}.

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