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Math Help - 3 Logic Statements

  1. #1
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    3 Logic Statements

    Any help understanding why these statements are true is appreciated:

    A.) If 8<3, then 22 = 5.

    B.) If 8 is even and 5 is not prime, then 4<7.

    C.) If both 5-3=2 and 5+3=2, then 9=4.
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  2. #2
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    Re: 3 Logic Statements

    Quote Originally Posted by Convrgx View Post
    Any help understanding why these statements are true is appreciated:

    A.) If 8<3, then 22 = 5.

    B.) If 8 is even and 5 is not prime, then 4<7.

    C.) If both 5-3=2 and 5+3=2, then 9=4.
    a) since 8 > 3, the then statement can be anything at all and the overall expression holds true.

    b) again, 5 is prime, so the then statement can be anything

    c) you should be getting the picture by now
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  3. #3
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    Re: 3 Logic Statements

    Any statement of the form "If A, then B" can be evaluated by a flow chart.

    \begin{matrix}\text{Is }A\text{ true?} & \stackrel{\text{Yes?}}{\longrightarrow} & \text{Is } B \text{ true?} & \stackrel{\text{Yes?}}{\longrightarrow} & \text{Statement is true.} \\ \downarrow \text{No?} & & \downarrow \text{No?} & & \\ \text{Statement is true.} & & \text{Statement is false.} & &\end{matrix}

    That's about it.
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  4. #4
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    Re: 3 Logic Statements

    Quote Originally Posted by Convrgx View Post
    Any help understanding why these statements are true is appreciated:
    A.) If 8<3, then 22 = 5.
    B.) If 8 is even and 5 is not prime, then 4<7.
    C.) If both 5-3=2 and 5+3=2, then 9=4.
    Here is an old logic teacher's trick.

    A false statement implies any statement.

    A true statement is implied by any statement.

    Look at the if statement if that is false look no further because the whole is true.

    Look at the then statement if that is true look no further because the whole is true.
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