Logic 101 (#16): Double Negation

This lecture begins our unit on replacement rules. Replacement rules allow us to freely transition between two logically identical expressions. This means we can erase complicated expressions and use simpler ones instead.

Here, the double negation rule says we can replace ~~p with just p, where p is a simple sentence or compound expression.

[Qattea]

So when people say “It’s not impossible” they are really saying “It’s possible”?

[anilover]

But what if I have ~(~p^q)? What law should I use? Is it the double negation law or the de morgans law?

[PunmasterSTP]

Double negation? More like "tons of information!"

...you make writing these puns too easy 😎

[abc]

Well I do encounter a Problem here. If P is "I can think", then ~P is "I cannot think" and ~~P is "I cannot not think". But "I cannot not think" is equivalent to "I am always thinking" and not to "I can think", isn't it? I don't know, where my mistake is...

[zorabura]

How would one prove the validity of  H v G, ¬(D & F) → ¬G, ¬(D v E) ∴ H