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Math Help - Truth table problem

  1. #1
    CPR
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    Truth table problem

    Is the following valid or invalid? (show by using a truth table).

    If Rick gains employment, then Rick will earn a paycheck. p->q
    If Rick earns a paycheck, then Rick will be excited. q->r

    Rick gains employment. p

    ____________________________
    Rick will be excited. r


    what is my final statement? Which is correct before completing my truth table?
    [p^(p->q)]^(q->r) or is it [p^(p->q)]^r
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by CPR View Post
    Is the following valid or invalid? (show by using a truth table).

    If Rick gains employment, then Rick will earn a paycheck. p->q
    If Rick earns a paycheck, then Rick will be excited. q->r

    Rick gains employment. p

    ____________________________
    Rick will be excited. r


    what is my final statement? Which is correct before completing my truth table?
    [p^(p->q)]^(q->r) or is it [p^(p->q)]^r
    P => R

    you want to know if gaining employment makes Rick excited in every instance
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  3. #3
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    Hello, CPR!

    Is the following valid or invalid? (show by using a truth table).

    If Rick gains employment, then Rick will earn a paycheck. . p \to q
    If Rick earns a paycheck, then Rick will be excited. . q \to r
    Rick gains employment. . p
    -----------------------------------------------
    Therefore: Rick will be excited. . r

    The argument is: . \bigg[(p \to q) \wedge (q \to r) \wedge p\bigg] \to r


    (The argument is valid; the final column should be eight T's.)

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  4. #4
    CPR
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    Thanks!

    Thanks for the help. I got it. I was on the right page. Perhaps you can help me with my post under Urgent Help. It is an Induction problem.
    It is 1+2+3....(4n-2)= n(3n-1)

    The basic step is n=1. 4(1)-2 = 1(3(1)-1)
    Induction step is:
    1+2+3....(4k-2) = k(3k-1)

    1+2+3....(4k-2)+(k+1) = k(3k-1) = (K+1)

    I'm having problems from this point. Please help!
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    Quote Originally Posted by CPR View Post
    Thanks for the help. I got it. I was on the right page. Perhaps you can help me with my post under Urgent Help. It is an Induction problem.
    It is 1+2+3....(4n-2)= n(3n-1)

    The basic step is n=1. 4(1)-2 = 1(3(1)-1)
    Induction step is:
    1+2+3....(4k-2) = k(3k-1)

    1+2+3....(4k-2)+(k+1) = k(3k-1) = (K+1)

    I'm having problems from this point. Please help!

    I think your k+1 is in the wrong place...if i'm correct, you would assume that
    1+2+3....(4k-2) = k(3k-1) for all n >= 1

    Then you want to prove:

    1+2+3....(4k-1) = k(3k)

    Can someone confirm i'm correct?
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  6. #6
    CPR
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    Instead of the last equal sign I meant to type =k(3k-1)+ (k+1)

    Yes that is what I got on my first attempt but where do I go from there.
    So after =(3k-K) + (k+1)
    = 3k +1
    now what? I need your help!
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  7. #7
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    Quote Originally Posted by CPR View Post
    Instead of the last equal sign I meant to type =k(3k-1)+ (k+1)

    Yes that is what I got on my first attempt but where do I go from there.
    So after =(3k-K) + (k+1)
    = 3k +1
    now what? I need your help!
    you want to prove:

    1+2+3....(4k-1) = (k+1)(3k)
    which equals
    1+2+3....(4k-1) = (3k^2 + 3k)

    So now rather than try to simplify it any further (like you did above), you need to prove that (4k-1) = (3k^2+3k)...so start from the left, and try to get the right. Don't start with what you want to prove..You will need to suppose that (4k-2) = k(3k-1) (This is your IH) and use it to prove k+1, so in your algebra, you want to get 4k-2, so you can say "I know that 4k-2 = k(3k-1) and therefore...blah blah blah"

    Use that and do the algebra to get (4k-1) = (3k^2+3k), don't forget about your IH which you'll need to complete the proof.
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  8. #8
    CPR
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    okay, I'm trying but its not working. I'll continue to try for awhile, but Im not getting it.
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  9. #9
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    Quote Originally Posted by CPR View Post
    okay, I'm trying but its not working. I'll continue to try for awhile, but Im not getting it.
    Try re-writing it using the summation notation, maybe that will help you understand it better?
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  10. #10
    CPR
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    What is summation notations?
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  11. #11
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by CPR View Post
    What is summation notations?
    writing a sum using the \sum symbol
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    please help me someone

    i need to constuct a truth table...but i absolutely cannot remember how!

    (pv~r)^~(qvr)
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  13. #13
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    Quote Originally Posted by malia View Post
    i need to constuct a truth table...but i absolutely cannot remember how!

    (pv~r)^~(qvr)
    Please start a new thread for a new question.

    -Dan
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  14. #14
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    Hello, malia!

    I can't give you a review on truth tables,
    . . but this is what you should have . . .


    \begin{array}{c|c|c|c|c|c|c|c|c|c|c}<br />
p & q & r & (p & \vee & \sim r) & \wedge & \sim & (q & \vee & r) \\ \hline<br />
T & T & T & T & T & F & {\color{blue}F} & F & T & T & T \\<br />
T & T & F & T & T & T & {\color{blue}F} & F & T & T & F \\<br />
T & F & T & T & T & F & {\color{blue}F} & F & F & T & T \\<br />
T & F & F & T & T & T & {\color{blue}T} & T & F & F & F \end{array}
    . \begin{array}{c|c|c|c|c|c|c|c|c|c|c}<br />
F & T & T & F & F & F & {\color{blue}F} & F & T & T & T \\<br />
F & T & F & F\, & T & \;\;T\:\; & {\color{blue}F} & F & T \,& T \,& F \\<br />
F & F & T & F & F & F & {\color{blue}F} & F & F & T & T \\<br />
F & F & F & F & T & T & {\color{blue}T} & T & F & F & F \\<br />
& & & ^1 & ^2 & ^1 & ^4 & ^3 & ^1 & ^2 & ^1<br />
\end{array}

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  15. #15
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Soroban View Post
    Hello, malia!

    I can't give you a review on truth tables,
    . . but this is what you should have . . .


    \begin{array}{c|c|c|c|c|c|c|c|c|c|c}<br />
p & q & r & (p & \vee & \sim r) & \wedge & \sim & (q & \vee & r) \\ \hline<br />
T & T & T & T & T & F & {\color{blue}F} & F & T & T & T \\<br />
T & T & F & T & T & T & {\color{blue}F} & F & T & T & F \\<br />
T & F & T & T & T & F & {\color{blue}F} & F & F & T & T \\<br />
T & F & F & T & T & T & {\color{blue}T} & T & F & F & F \end{array}
    . \begin{array}{c|c|c|c|c|c|c|c|c|c|c}<br />
F & T & T & F & F & F & {\color{blue}F} & F & T & T & T \\<br />
F & T & F & F\, & T & \;\;T\:\; & {\color{blue}F} & F & T \,& T \,& F \\<br />
F & F & T & F & F & F & {\color{blue}F} & F & F & T & T \\<br />
F & F & F & F & T & T & {\color{blue}T} & T & F & F & F \\<br />
& & & ^1 & ^2 & ^1 & ^4 & ^3 & ^1 & ^2 & ^1<br />
\end{array}

    nice use of LaTeX, that must have taken you forever!
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