We define on N the relation by mnm divides n. Prove that is a partial order...

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We define on N the relation by mnm divides n. Prove that is a partial order on N. Let f: X→→Y be a function. Suppose that there are two functions g, h: Y→X such that for all EX, (gof)(x)=x, and for all y Y, (foh)(y) = y. (a) Prove that f is bijective. (b) Prove by contradiction that g = h. [10 points] [10 points] We define on N the relation by mnm divides n. Prove that is a partial order on N. Let f: X→→Y be a function. Suppose that there are two functions g, h: Y→X such that for all EX, (gof)(x)=x, and for all y Y, (foh)(y) = y. (a) Prove that f is bijective. (b) Prove by contradiction that g = h. [10 points] [10 points]