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Math Help - negations

  1. #1
    Senior Member
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    negations

    Negate this sentence: If n is prime, then n is odd or n is 2.

    I know the purpose is to just to negate the sentence no matter what.

    The negation solution is: n is a prime and n is even and n is not 2.

    So in discrete math, it doesn't matter if this is really true or not? its just an example???

    i don't think its possible to have n be prime, and alos be even at the same time, if its not 2.

    thanks for help with this.
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  2. #2
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    Hello, rcmango!

    Negate this sentence: . \text{ If }n\text{ is prime, then }n\text{ is odd or }n\text{  is 2.}

    We have: . (n\text{ prime}) \rightarrow \bigg[(n\text{ odd}) \vee (n = 2)\bigg]

    which is equivalent to: . \sim\!(n\text{ prime})\; \vee\: (n\text{ odd}) \:\vee\: (n=2)


    The negation is: . n\text{ odd}) \:\vee \n=2)\bigg] " alt="\sim\bigg[\sim\!(n\text{ prime}) \:\vee \n\text{ odd}) \:\vee \n=2)\bigg] " />

    . . . . . . . . . . \Longleftrightarrow\;\;(n\text{ prime)}\; \:\wedge \:\sim\!(n\text{ odd}) \;\wedge \:\sim\!(n = 2)

    . . . . . . . . . . \Longleftrightarrow\;\;(n\text{ prime})\;\wedge \;(n\text{ even}) \;\wedge\;(n \neq 2)

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