# Logical equivalencies involving ifs and nors

## Main Question or Discussion Point

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.

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haruspex
Homework Helper
Gold Member
The trick is to obtain a NOT function by p NOR p. That breaks the symmetry.

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