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Logical equivalencies involving ifs and nors

  1. Oct 15, 2012 #1
    Can anyone solve this step by step, so I can see how it's done? I've been at for a while now and can't seem to get it. Here's the problem:

    Find a compound proposition logically equivalent to p → q using only the logical operator ↓.

    Thanks for the help. I'm really trying to get this stuff, but it's not coming easy.
     
  2. jcsd
  3. Oct 15, 2012 #2

    haruspex

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    The trick is to obtain a NOT function by p NOR p. That breaks the symmetry.
     
  4. Oct 15, 2012 #3
    Thanks for the suggestion, I finally got it.

    If anyone's interested:

    p → q
    ≡ ¬p ∨ p this is one of the common equivalencies given in my book by Deitel
    ≡ ¬(¬p ↓ p) this equivalency was found in a previous exercise
    ≡ ¬((p ↓ p) ↓ q) by ¬p ≡ p ↓p
    ≡ ((p ↓ p) ↓ q) ↓ ((p ↓ p) ↓ q) by ¬p ≡ p ↓p
     
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