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Math Help - Condition/Truth Table

  1. #1
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    Exclamation Condition/Truth Table

    Does anybody have any idea about this stuff?
    Are the 2 conditions equivalent? Explain why.
    a. Not(a<=b)
    (a>=b) OR Not (a=b)




    b. Not(a<=b)
    (a>=b) AND Not (a=b)




    Write a condition equivalent to the negation of the given condition, and that does not use the NOT operator.
    a. a<b




    b. (a>b) And (c<>d)




    c. (a=b) Or (a=c)
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  2. #2
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    Hello, melwin!

    Are the 2 conditions equivalent? Explain why.

    \text{(a)}\;\text{ Not }(a \leq b)

    . . (a \geq b)\text{ or Not } (a=b)

     a \leq b means: (a is less than b) or ( a equal to b.)

    Its negation is: . \sim(a \leq b) \quad=\quad\sim\bigg[(a\text{ is less than }b) \text{ or } (a = b)\bigg]

    By DeMorgan's Law, this is: . \sim(a\text{ is less than }b)\:\text{ and }\sim(a - b)

    . . . . . . . . . . . . . . . . =\;(a\text{ is greater than or equal to }b)\;\text{ and }\:(a \neq b)

    . . . . . . . . . . . . . . . . . . . . =\;(a \geq b) \text{ {\color{red}and} Not }(a = b)


    This is not what the second statement says; they are not equivalent.




    \text{(b)}\;\text{Not }(a \leq b)

    . . (a \geq b)\text{ and Not }(a = b)

    These two are equivalent . . . see part (a).




    Write a statement equivalent to the negation of the given condition
    that does not use the NOT operator.

    \text{(a)}\;a < b

    \sim(a < b) \quad\Longrightarrow\quad a \geq b



    \text{(b) }\;(a>b) \wedge (c \neq d)

    \sim\bigg[(a > b) \wedge (c \neq d)\bigg] \quad\Rightarrow\quad \sim(a > b)\: \vee \sim(c \neq d) \quad\Rightarrow\quad (a \leq b) \vee (c = d)<br />



    \text{(c) }\;(a=b) \vee(a=c)

    \sim\bigg[(a=b) \vee (a = c)\bigg] \quad\Rightarrow\quad \sim(a=b)\: \wedge \sim(a = c) \quad\Rightarrow\quad (a \neq b) \:\wedge (a \neq c)<br /> <br />

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  3. #3
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    hm

    So both question 1 and 2 are true?
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