2.14

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.

b) If a person buys at least 400 cups of coffee in a year, then there is at least one day in which the person has bought at least two cups of coffee.

Prove each of the following statements using a direct proof.

(b) For any positive real numbers, x and y, x+yxy (xy is underneath square root)

(c) If x is a real number and x 3, then 12 - 7x + x² 0.

please answer all question, and show work clearly