Prove that y x yx x zSolutionz E Rx E R y E R y x yx

Solution

z E R:(x E R+ : ( y E R : [ y -x = y/x <=> x!=z ])))

so here z,y can be any number and x must be a positive number

let us take x =4 , y = 6 z = 3

6- 4 = 6/3 <=> 4!=3

2 =2 <=> 4!=3

true <=> true

so it is true

let us prove it for negative values

x= 3

y=-1

z=3

now -1-3 = -1/3 <=> 3!=3

        false <=> false

       is true