Exercise 1. [Used in Theorem 1.5 and Theorem 15.] Letre Z and y e Z. (1) Prove that (x, y)] = 0 if and only if r= 0. (2) Prove that (x, y)] = 1...

Help soving ONLY part (1).... Using theorem 1.5.5 and 1.5.6 prove (1)

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Exercise 1.5.3. [Used in Theorem 1.5.5 and Theorem 15.6.] Letre Z and y e Z".(1) Prove that (x, y)] = 0 if and only if r= 0.(2) Prove that (x, y)] = 1 if and only ifx = y.(3) Prove that 0 < [(x. y)] if and only if 0 < xy.