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Math Help - Logic Question

  1. #1
    Member RedBarchetta's Avatar
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    Logic Question

    "Another true statement about real numbers is the following: If x^2<0, then x=23."

    How is this a true statement?
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  2. #2
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    Quote Originally Posted by RedBarchetta View Post
    "Another true statement about real numbers is the following: If x^2<0, then x=23."

    How is this a true statement?
    I think it is true because x^2 <0 given x \in R is false, and in mathematics if the hypothesis is false, then the statement is true no matter what the following of that hypothesis is.
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  3. #3
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    Quote Originally Posted by RedBarchetta View Post
    "Another true statement about real numbers is the following: If x^2<0, then x=23."

    How is this a true statement?
    Let p= x^2<0 ,and q= (x=23) and by the definition of a conditional statement if a true p, implies a false q, then the statement p----->q is false. IN all the other cases p----->q is true.

    Since in our case p is false irrespectively of what q is ( x could be 23 or not) p---->q is true.

    The above is a semantical definition of the conditional statement:

    ...................p------>q................................................ .........................................
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  4. #4
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    Re: Logic question

    Quote Originally Posted by RedBarchetta View Post
    "Another true statement about real numbers is the following: If x^2<0, then x=23."

    How is this a true statement?
    The statement says that for any real x such that x^2 is negative, x is 23. That is false if and only if there is some x so that x^2<0 but x is not 23. There is no such x so the statement is true (vacuously).

    There is a free download of a book here, which walks through additional similar examples in detail (see the first part on logic and sets):
    Bobo Strategy - Topology
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