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Math Help - Sketch the graph of P and Q

  1. #1
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    Sketch the graph of P and Q

    P = x < 10/3
    Q = -2 < or = x < or = 6


    On a number line, sketch the graph of:

    P:

    Q:

    P V Q:

    P ^ Q:

    (P V Q)':


    I had this problem on a test, and i need to see if i got them right! thanks

    oh and this one also:

    state the negation of "3 + 2 = 5 or 10<2"
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by NeedHelp18 View Post
    P = x < 10/3
    Q = -2 < or = x < or = 6


    On a number line, sketch the graph of:

    P:

    Q:

    P V Q:

    P ^ Q:

    (P V Q)':
    it would be hard to draw these here

    maybe Soroban can do it

    I had this problem on a test, and i need to see if i got them right! thanks

    oh and this one also:

    state the negation of "3 + 2 = 5 or 10<2"
    Let P and Q be statements. then,

    \neg (P \vee Q) = \neg P \wedge \neg Q

    now can you do it?
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  3. #3
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    Hello, NeedHelp18!

    Don't stick in equal-signs so carelessly . . .



    P\!:\;\;x < \frac{10}{3}

    Q\!:\;\;-2 \leq x \leq 6

    On a number line, sketch the graph of:

    (a)\;P
    . . . . x < \frac{10}{3}


    . . ======o-----
    . . . . . . . . . . ^{\frac{10}{3}}



    (b)\;Q
    . . . . -2 \leq x \leq 6


    . . --\bullet======\bullet--
    . . . . . ^{\text{-}2}\qquad\qquad\quad\; ^6



    (c)\;P \vee Q
    . . . . \left(x < \frac{10}{3}\right)\:\text{ or }\:(-2 \leq x \leq 6)\quad\Rightarrow\quad (x \leq 6)


    . . =====\bullet--
    . . . . . . . . . ^6



    (d)\;P \wedge Q
    . . . . \left(x < \frac{10}{3}\right)\:\text{ and }\:(-2 \leq x \leq 6)\quad\Rightarrow\quad \left(-2 \leq x < \frac{10}{3}\right)


    . . --\bullet====o--
    . . . . . ^{\text{-}2}\qquad\quad\;\; ^{\frac{10}{3}}



    (e)\;(P \vee Q)'
    . . . . (x \leq 6)'\quad\Rightarrow\quad (x > 6)


    . . ---o====
    . . . . . . . ^6




    State the negation of: .(3 + 2 = 5) or (10 < 2)

    . . \text{(3 + 2}\neq 5)\:\text{ and }\:(10 \geq 2)


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