# Logical equivalencies involving ifs and nors

1. Oct 15, 2012

### nicnicman

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. Oct 15, 2012

### haruspex

The trick is to obtain a NOT function by p NOR p. That breaks the symmetry.

3. Oct 15, 2012

### nicnicman

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