The base concepts of logic are the conjunction, disjunction, negation and the implication.
Part 1 – The negation
In logic, a simple statement can only have 2 meanings. Either it is the case, which is called ‘true’, or it is not the case, which is called ‘false’. ~p is read as ‘it is not the case that p’.
p And ~p together form a context. If p=T, then ~p=F; and conversely, if ~p=T, then p=F. Since p and ~p exclude each other, they are each other’s complement.
negation | p=the roofs get wet | meaning | |
~ |
p |
||
F |
T |
The roofs get wet | p is T, so ~=F ⇒ p=T |
T |
F |
It is not the case that the roofs get wet | p is F, so ~=T ⇒ p=F |
Double negation
In propositional logic, the negation of p‘s negation, is the same as p. Not not p is equivalent to p, expressed in logical symbols: ~~p ≡ p.