CS201 Homework 2

Quiz problems

(Rosen 3.1; 8d) What relavent conclusion or conclusions can be drawn... "Every student has an internet account..."

(Rosen 3.1; 8e) What relavent conclusion or conclusions can be drawn... "All foods that are healthy to eat do not taste good..."

(Rosen 3.1; 10d) Explain which rules of inference are used for each step. "There is someone in this class who has been to France..."

(Rosen 3.1; 16c) Prove that the square of an even number is an even number using a proof by contradiction.

(Rosen 3.1; 26) Prove or disprove that 2^n + 1 is prime for all nonnegative integers n.

(Rosen 3.1; 30) Prove that the square of an integer not divisible by 5...

Problems to turn in

(Rosen 3.1; 8c) What relavent conclusion or conclusions can be drawn... "All insects have six legs..."

(Rosen 3.1; 16a) Prove that the square of an even number is an even number using a direct proof.

(Rosen 3,1; 16b) Prove that the square of an even number is an even number using an indirect proof.

(Rosen 3.1; 20) Prove that the sum of two rational numbers is rational.

Extra Credit

I have two children, each of which are more than one year old. I told my friend, Mr. P, the product of ages of my two children. Then I told my other friend, Ms. S, the sum of the ages of my two children. Then I left the room, and they had the following conversation:

Mr. P: I don't know the ages of Karl's children.
Ms. S: I knew you wouldn't.
Mr. P: Aha! Now I know them.
Ms. S: Aha! Now I know them too.

So... How old are my kids?