Question

If x and y are two rational numbers such that x > y, then x – y is always a positive rational number. True or False? Why?

Answer 1

true

 x = p / q
y = r / s

x > y  =>  p  / q  > r  / s
let them be written such that q and s are positive.  p and r can be positive or negative.

Multiply with   q s   on both sides
=>     p s >  r q

p /q - r / s  =    [ p s - r q ] / q s
                 > 0  as  ps > rq and  qs  > 0

Answer 2

Answer:

Step-by-step explanation:

true

 x = p / q

y = r / s

x > y  =>  p  / q  > r  / s

let them be written such that q and s are positive.  p and r can be positive or negative.

Multiply with   q s   on both sides

=>     p s >  r q

p /q - r / s  =    [ p s - r q ] / q s

                > 0  as  ps > rq and  qs  > 0

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