Suppose $a,b∈\mathbb{R}$ use proof by contrapositive to show the following implication is true $b^3+ba^2\leq a^3+ab^2 \Rightarrow b\leq a$ Suppose $\\{a,b\\}\subset \mathbb{R}$ use proof by contraposition to show the following implication is true : $$b^3+ba^2\leq a^3+ab^2 \Rightarrow b\leq a$$ using contraposition me is we start $a \leq b$

For $ab=0$ it's obvious.

Let $ab\
eq0$ and $b>a$.

Thus, $$b^3+a^2b-a^3-ab^2=(b-a)(a^2+b^2)>0.$$ We got a contradiction.