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Negation (or Denial)

The process of forming the contradictory of a given statement is called negation.
The statement contradicting a given statement p is denoted by ~p. If p is true then ~p must be false and if p is false then ~p must be true since they are contradictory. As an example if p: prices are rising, then ~p: prices are not rising. Here, ~p can also be written as “It is not true that prices are rising”. or as “It is false that prices are rising”. or as “It is not the case that prices are rising”.
Truth table (~p)
~ (~p)
Rule: ~p is true only when p is false.
It may be noticed that ~(~p) = p. Also p and ~p are not contrary. For example, the statements “x is an even number” and “x is an odd number” are contrary if x is a whole number because both the statements cannot have the same truth value.
It may be observed that negation is not a binary operation, it is a unary operation, i.e., a modifier.
  1. ~p is true iff p is false.
  2. ~p is false iff p is true.

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