Determine whether each of the following statements is true or false. For each false statement give a counterexample.
a) If f:A →B and (a, b), (a, c) ∈ f, then b = c.
b) If f: A B is a one-to-one correspondence and A, B are finite, then A = B.
c) If f: A → B is one-to-one, then f is invertible.
d) If f: A → B is invertible, then f is one-to-one.
e) If f:A →B is one-to-one and g, h: B → C with go f = h o f, then g = h.
f) If f : A → B and A1, A2 ⊂ A, then f(A1 ∩ A2) = f(A1 ∩ f(A2).
g) If f: A → B and B1, B2 ⊂ B, then f-l(B1 ∩ B2) = f-1 (B1) ∩ f-1(B2)