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Math Help - Contradiction, counterexample, when and how to use each form of proof and disproof?

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    Contradiction, counterexample, when and how to use each form of proof and disproof?

    CounterExample can be used to disprove a universal statement saying something like "For all integers....if [something] then [something]" a way to counterexample is to simply find one situation or one set of numbers where the statement is false.

    Can someone explain to me how to use contradiction?


    Also, what would you use in situation where the statement is completely false? counter example wont really work for that.... I was wondering if something like this will ever pop up during a typical discrete mathematics course?
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    MHF Contributor harish21's Avatar
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    Quote Originally Posted by matthayzon89 View Post
    CounterExample can be used to disprove a universal statement saying something like "For all integers....if [something] then [something]" a way to counterexample is to simply find one situation or one set of numbers where the statement is false.

    Can someone explain to me how to use contradiction?


    Also, what would you use in situation where the statement is completely false? counter example wont really work for that.... I was wondering if something like this will ever pop up during a typical discrete mathematics course?
    Using contradiction means that you assume that the statement is false and start working on it until derive a contradiction. A good example I would suggest looking at is the proof of the statement that "There is no rational number whose square root equals 2"
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