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Thread: tautology ,contradiction or neither

  1. #1
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    tautology ,contradiction or neither

    Write down the truth table for the compound proposition(p -> q) ->((p V r ) ->(q Vr )) :Is this a tautology, a contradiction or neither?
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  2. #2
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    Re: tautology ,contradiction or neither

    What have you done on this? Do you see that there will be 8 "cases", 8 rows in your truth table? How many columns there are depends upon how you want it "divided". Personally, I would start with three columns for the various values of r, s, and t, then a column for p-> q, a column for (p v r), a column for (q v r), a column for (p v r)-> (q v r), and finally, a column for the entire statement.

    Now, do you know what a "tautology" and a "contradiction" are?
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    Re: tautology ,contradiction or neither

    Hey Halls of Ivy ,
    sorry had a pretty big day and fell asleep in the evening ,I'll attempt this tomorrow morning ( about 10 hours from now) and post my working .
    Cheers ...
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    Re: tautology ,contradiction or neither

    Quote Originally Posted by bee77 View Post
    Write down the truth table for the compound proposition(p -> q) ->((p V r ) ->(q Vr )) :Is this a tautology, a contradiction or neither?
    Good day Bee. Here is a tool that may help you with constructing truthtables.

    Have you been shown how truthtables are constructed?
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    Re: tautology ,contradiction or neither

    My answer
    p. q. r........ (p->q)... (p v r) ...(q v r ) ...(p v r )->(q v r ) ...(p->q)->((p v q)->(q v r) )

    F.F.F...............T........... F.......... F.................... T............................. T
    F .F.T.............. T.......... T ..........T ...................T.............................. T
    F. T. F ..............T .........F ......... T................... T ...............................T
    F .T. T.............. T .........T ...........T.................. T ...............................T
    T. F. F.............. F......... T............ F................. F ................................T
    T. F .T.............. F .........T ...........T................. T................................. T
    T. T. F.............. T ........T ............T................. T ................................T
    T. T. T............... T........T............. T................ T..................................T
    .
    I'm guessing it's Tautology because the whole statement is true regardless of the value of the individual statements.
    Contradiction means it would contradict and be opposites of the truth values ..(I just put dots in to separate the truth values )
    Hmm Is my answer ok ?...thanks
    Last edited by bee77; Aug 22nd 2017 at 05:18 PM.
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    Re: tautology ,contradiction or neither

    Quote Originally Posted by bee77 View Post
    My answer
    p q r (p->q) (p v r) (q v r ) (p v r )->(q v r ) (p->q)->((p v q)->(q v r) )

    F F F T F F T T
    F F T T T T T T
    F T F T F T T T
    F T T T T T T T
    T F F F T F F T
    T F T F T T T T
    T T F T T T T T
    T T T T T T T T

    I'm guessing it's Tautology because the whole statement is true regardless of the value of the individual statements.
    Contradiction means it would contradict and be opposites of the truth values ..
    Hmm Is my answer ok ?...thanks
    Why are you guessing?
    The last column consists of all true truth values. So no matter how one assigns the values the result is true.
    What do we call such a sentence?
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  7. #7
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    Re: tautology ,contradiction or neither

    G'day Plato chuck another shrimp on the barbie
    ok it's Tautology as the results are all True.
    Thanks Plato . Yes I just saw your post as I was putting in the table separating it with dots ...
    Thanks for the tool that helps with Truth tables
    Last edited by bee77; Aug 22nd 2017 at 05:22 PM.
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