Proving Equivalence of Rational Number Statements

[ArtyJay9]

Show that these statement about real number x are equivalent
(i) x is rational
(ii) x/2 is rational
(iii)3x-1is rational

i think you have to use contradiction but i don't know how

 

[Office_Shredder]

x is rational if and only if you can write it in the form p/q for p, q integers (and q non-zero). So if x is rational, let x=p/q. Can you find integers m and n such that x/2=m/n? You can do this exact process to show that 1 implies 2, 2 implies 3, and 3 implies 1 (which gives that they are equivalent)