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Thread: proofs.

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by kiddopop View Post

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

    Here is there sum x+x+1+ x+2= 3x+3

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

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