It is required that you show your work. When doing proofs, each step must use only one law, rule of inference, or equivalence. The law, rule, or equivalence used on each step must be stated. Make sure that your writing is legible, or else, please type your answers. Submit your solution on Canvas.

1. (10 points) Prove that if n is an integer and 3n + 6 is odd, then n is odd.

2. (10 points) Prove that 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.