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Math Help - Rewriting expressions with logic laws (2)

  1. #1
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    Rewriting expressions with logic laws (2)

    Rewrite: (p \wedge (q \to (p \vee (p \wedge q)))) \wedge q and determine if its tautology, contradiction or neither. Using truth table I got neither.

    My working out:

    - (p \wedge (q \to (p \vee (p \wedge q)))) \wedge q
    - (p \wedge (q \to p)) \wedge q
    - (p \wedge (\sim q \vee p)) \wedge q
    - (p \wedge (p \vee \sim q)) \wedge q
    - ((p \wedge p) \vee \sim q) \wedge q
    - (p \vee \sim q) \wedge q

    Now im a little stuck. After the truth table, im assuming I have to finish off with just a "p". Any help would be much appreciated.
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  2. #2
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    Hi

    Since your formula has the form A\wedge q, finding only p will be hard.

    In your other post, you used p\wedge(p \vee\neg q)\equiv p. Applying this to your third or fourth line will allow you to conclude.

    (What you did for line 4 \rightarrow line 5 is wrong)
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  3. #3
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    Quote Originally Posted by clic-clac View Post
    Hi

    Since your formula has the form A\wedge q, finding only p will be hard.

    In your other post, you used p\wedge(p \vee\neg q)\equiv p. Applying this to your third or fourth line will allow you to conclude.

    (What you did for line 4 \rightarrow line 5 is wrong)
    Thanks for your help, but I will only end up with  p \wedge q and not p. Is that still fine?
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  4. #4
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    Yes, I suggest you redo your table.
    Note that even if p is true, as soon as q is false, the formula is false; thus the formula cannot be equivalent to p!
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  5. #5
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    Quote Originally Posted by clic-clac View Post
    Yes, I suggest you redo your table.
    Note that even if p is true, as soon as q is false, the formula is false; thus the formula cannot be equivalent to p!
    Are you referring to the truth table? To re-do it?
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