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Discrete Math question on creating a logically equivalent compound proposition

  1. Sep 29, 2012 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant equations

    3. The attempt at a solution
    My book does not go into much detail about solving this problem other than providing the answer. I really want to know how to get the answer, step by step. If it helps, here is the answer: ((p ↓ p) ↓ p) ↓ ((p ↓ p) ↓ p)

    I've tried constructing truth tables, but that's not really helping.
    How in the world would I derive the above answer?
  2. jcsd
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