[size=150]Proposition: Suppose x ∈ Z. If x[sup]2[/sup] −6x+5 is even, then x is odd.[br][br]Proof. (Contrapositive) Suppose x is (a)__________________________.[br][br]Thus x is even, so (b)________________________ for some integer a.[br][br]So x[sup]2 [/sup]- 6x+5 [br] =(2a)[sup]2[/sup]−6(2a)+5[br] = 4a[sup]2[/sup]−12a+5[br] = 4a[sup]2[/sup]−12a+4+1[br] = 2(2a[sup]2[/sup]−6a+2)+1.[br][br]Therefore x[sup]2[/sup] −6x+5 = 2b +1, where b is the integer (d)________________________[br][br]Consequently x[sup]2[/sup] −6x+5 is (e)____________________.[br][br]Therefore x[sup]2[/sup] −6x+5 is (f)________________________[/size].

[size=150]Use the method of contrapositive proof to prove the following statement:[br]Suppose x, y ∈ R. If y[sup]3[/sup] + yx[sup]2[/sup] ≤ x[sup]3[/sup] + x y[sup]2[/sup], then y ≤ x.[/size]