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Question: using these axioms please prove parts a and b from...

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Using these axioms, please prove parts a and b from #7The set of rational numbers, Q, is defined to be the smallest set that satisfies all of the following axioms: If z,y E Q then +yEQ and ry E Q. (Closure under addition and multiplication) and distributive 0 Esuch that for all x EQ, +0-x. (Additive identity) (Additive inverses) (Multiplicative identity) (1/r)-1. (Multiplicative inverses) For al r, y EQ exactly one of the following statements is true: . Addition and multiplication in are commutative, associative, . For all x E Q, there exists-x E Q such that z (-)- 0. ·I E Q with 1メ0, such that for all x E Q, we have lx = x . For all Q, with xメ0, there exists l/x € Q such that z- x<y, x=y, y<x, where x < y implies 0 < y-x . For all x, y,2E Q, if x < y and y < z then x < z. (This property and the previous one say that Q is totally ordered) . For all z,y,z EQ, if y < z then y<+2 . For all x, y E Q, if x > 0 and y > 0 then xy > 0 7. Use the axioms for above to prove the following: (a) For all a, b E Q, there exists some c E Q such that a + c b. (You should be able to make a pretty good guess about what c is, then just show that a +c must equal b.) (b) For all r, s E Q with rメ0, there exists t E Q such that rt-8

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