2.23

Prove each statement. By us proof of contrapositive

(a) For every integer n, if n² is an odd, then n is odd.

(b) For every integer x, if x² - 2x + 7 is even, then x is odd.

(c) If x and y are real numbers and x + y is irrational, then x is irrational or y is irrational.

2.41

Give a proof for each statement. Proof by using proof of contradiction

(a) If a group of 9 kids have won a total of 100 trophies, then at least one of the 9 kids has won at least 12 trophies.