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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 #12The set of rational numbers, Q, is defined to be the smallest set that satisfies all of the following axioms: If z,y Ethen +yEQ and ry E Q. (Closure under addition and multiplication) . Addition and multiplication in Q are commutative, associative, and distributive. . 0 E Q such that for all | E Q, x + 0-x. (Additive identity) ● For all z E Q, there exists-z E Q such that x + (-x) 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 E Q such that z- . For all , y EQexactly one of the following statements is true: (Additive inverses) (Multiplicative identity) (1/r)-1. (Multiplicative inverses) x<y, x=y, y<x, where x < y implies 0 < y-x For a x,y, z E Q, if < y and y < z then < z. (This property and the previous one say that Qis totally ordered) . For all x,y,z EQ, if y< z then x+y<a+ 2 . For all x, y E Q, if x > 0 and y > 0 then xy > 0 12. Let r,s EQ (a) Ifr> 0 then 1/r>0 and if r <0 then 1/r <0 (b) If 0 < T< s, then 0 < 1/s< 1/r.

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