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Homework Help: Help, using Truth Table prove that the following logic statement is a Tautology

  1. Aug 30, 2010 #1
    1. The problem statement, all variables and given/known data

    By providing a truth table, show that the following logic statement is a tautology:

    p ∧ (p → q) → q


    Any help will be much appreciated.

    Thank You
     
  2. jcsd
  3. Aug 30, 2010 #2

    Mark44

    Staff: Mentor

    I would set up a truth table with columns for p, q, and p ==> q. You know how many rows you need, right?
     
  4. Aug 30, 2010 #3
    p | q | P → q
    -------------
    T | T | T
    T | F | F
    F | T | T
    F | F | T

    Thank you Mark44 but I don't think this is the correct answer/method as the output has to be true in all cases in order for it to be labeled a tautology. Any other suggestions?
     
  5. Aug 30, 2010 #4

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    You are missing at least one column, multiple columns if you want to break things down.
     
  6. Aug 30, 2010 #5
    D H could you give me an example please as I am new to logic...
     
  7. Aug 30, 2010 #6

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    You have the truth table for implication. p→q obviously is not a tautology. You weren't asked to show that. You were asked to show that p∧(p→q)→q is a tautology. Your truth table needs to end with a p∧(p→q)→q column on the right and with all four values in this column being T.
     
  8. Aug 31, 2010 #7
    Thank you DH, that was very helpful. My final question is, does it matter which way we write down the truth table?

    e.g.

    which one is correct?

    p | q | P → q | p∧(p→q)→q
    ---------------------------
    T | T | T | T
    T | F | F | T
    F | T | T | T
    F | F | T | T

    OR

    p | q | P → q | p∧(p→q)→q
    ---------------------------
    F | F | T | T
    F | T | T | T
    T | F | F | T
    T | T | T | T
     
  9. Aug 31, 2010 #8

    D H

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    Staff Emeritus
    Science Advisor

    You aren't going to get points for that. At least I hope you aren't. There is a thing called showing your work.
     
  10. Aug 31, 2010 #9

    Mark44

    Staff: Mentor

    To answer your question about the order, it doesn't really matter, but these are usually presented with the top row being T T ... and the bottom row being F F ...
     
  11. Aug 31, 2010 #10
    Thank You Mark44. You have been great!
     
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