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Symbolic Logic - Negation

statement friendly false true

Negation is another logical "operation." Unlike conjunction and disjunction, however, it is applied to a single statement. If one were to say, "She is friendly," the negation of that statement would be, "She is not friendly." The symbol for negation is " ~." It is placed in front of the statement to be negated, as in ~ (pΛq) or ~ p. If p were the statement, "She is friendly," ~ p means "She is not friendly," or more formally, "It is not the case that she is friendly." Prefacing the statement with, "It is not the case that...," avoids embedding the negation in the middle of the statement to be negated. The symbol lips is read "not p."

The statement ~ p is true when p is false, and false when p is true. For example, if p is the statement "x < 4," ~ p is the statement "x ≥ 4." Replacing x with S makes p false but ~ p true. If a boy, snubbed by the girl in "She is friendly," were to hear the statement, he would say that it was false. He would say, "She is not friendly," and mean it.


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