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Using field axioms, prove the following theorems: (i) If x and y are non-zero real numbers,...

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Advance Math

Using field axioms, prove the following theorems:

(i) If x and y are non-zero real numbers, then xy does not equal0

(ii) Let x and y be real numbers. Prove the followingstatements

1. (-1)x = -x

2. (-x)y = -(xy)=x(-y)

3. (-x)(-y) = xy

(iii) Let a and b be real numbers, and x and y be non-zero realnumbers. Then a/x + b/y = (ay +bx)/(xy)

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