Logic (10) – The fundamental logical concepts

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 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: ~~pp.

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