1. For all x, y Z prove the following: (a) -(-x) = x, (b) (-1)-x=...

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1. For all x, y € Z prove the following: (a) -(-x) = x, (b) (-1)-x= -x, (c) -(x + y) = -x + (-y), (d) (-x) y=x (-y) = (x+y), (e) (-x) (-y) = x. y. 2. Prove that for all y, z € Z, the equation x + y = z has a unique solution. 1. For all x, y € Z prove the following: (a) -(-x) = x, (b) (-1)-x= -x, (c) -(x + y) = -x + (-y), (d) (-x) y=x (-y) = (x+y), (e) (-x) (-y) = x. y. 2. Prove that for all y, z € Z, the equation x + y = z has a unique solution.

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1 a x x x b 1 x x c xyxyxy d x y x y xy e x 1 xy 2 Let y z be arbitrary elements of Z We will s... View the full answer