9. a. Prove the following statement: Ifr^{3}is irrational, thenris irrational. (by contrapositive)

b. Disprove the converse of the statement in part (a).

a) let r be rational number

$\displaystyle r=\frac{a}{b}$ for $\displaystyle a,b \in \mathbb{Z};b \neq 0$

$\displaystyle r^3=\frac{a^3}{b^3}$

$\displaystyle a^3r^3=b^3 \rightarrow a*a*a*r*r*r=b*b*b$

by definition integers are closed under multiplication, all integers are rational

therefore r^3 is rational

b) converse is if r is irrational then r^3 is irrational

counterexample??