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4. Let f be a one-to-one function from X into Y and let A C X. Show that f-1 (f (A)) = A. Give an exanmple showing that equality need not hold if f is not one-to-one. 5. Let f be a function from X onto Y and let B C Y. Show that f(f (B)- B. Give an example showing that equality need not hold if f is not onto Y 6. Prove Proposition 1.12. 7. Let f be a function from X into Y. Let g be a function from Y into Z Assume that g o f is one-to-one. Prove that f is one-to-one. Give an example showing that g need not be one-to-one 8. Let f be a function from X into Y. Let g be a function from y into Z Assume that g o f is onto Z. Prove that g is onto Z. Give an example showing that f need not be onto Y. 9. Find a bijection from (0. o0) onto (0. 1), with a cb. F
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