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Math Help - Define A, B in this proof

  1. #1
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    Define A, B in this proof

    I need to figure out what my A is and what my B is.

    The question is:

    Prove by contrapositive that 1+sqrt(2) is irrational. So how do I define my A and B.

    all I can think of is A: consider two numbers 1 and sqrt(2)
    B: their sum is irrational.

    I can prove it but I feel like my A and B are completely wrong. Thanks so much
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  2. #2
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    Contrapositive

    Hello meg0529
    Quote Originally Posted by meg0529 View Post
    I need to figure out what my A is and what my B is.

    The question is:

    Prove by contrapositive that 1+sqrt(2) is irrational. So how do I define my A and B.

    all I can think of is A: consider two numbers 1 and sqrt(2)
    B: their sum is irrational.

    I can prove it but I feel like my A and B are completely wrong. Thanks so much
    A is " \sqrt{2} is irrational"; B is " (1+\sqrt{2}) is irrational".

    The contrapositive of (A \Rightarrow B) is (\neg B \Rightarrow \neg A).

    \neg B \Rightarrow \neg A is If " (1 + \sqrt{2}) is not irrational, then \sqrt{2} is not irrational". This is correct, since (1+x) is rational \Rightarrow x is rational.

    Hence A \Rightarrow B, and (1+\sqrt{2}) is therefore irrational, since A is true.

    Grandad
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