1. ## proofs.

I'm having quite a bit of trouble with proofs.

(1) Prove using the contrapositive approach: If x is positive then so is x + 1.

(2) Let x and y be positive integers. Prove that x<y if and only if x^2 < y^2.

(3) Prove using cases that the sum of 3 consecutive integers is divisible by 3.

I just don't get proofs.

2. Originally Posted by kiddopop

(3) Prove using cases that the sum of 3 consecutive integers is divisible by 3.
Here are 3 consecutive numbers: $\displaystyle x,x+1, x+2$ where x is an integer.

Here is there sum $\displaystyle x+x+1+ x+2= 3x+3$

Now any number mulitplied by 3 is then also divisible by 3 would you agree?

So factoring $\displaystyle 3x+3 = 3(x+1)$ which has the form 3 times some number and therefore is divisible by 3.

3. Do you get definitions? Often that is the problem. The first problem suggests you prove the contrapositive. What is the contrapositive of a theorem in general- what is the definition of "contrapositive"? What is the contrapositive of this particular statement?