![]() " serves the same function as the logical negation symbol. The English expression "It is not the case that. ¬(p V q): The lion is not roaring and the birds are chirping ![]() ¬(p V q): Neither the lion is roaring nor the birds are chirping Its meaning can be represented by this truth table: p But if the original is false, the ¬ statement becomes true. So, if the original is true, the ¬ statement is false. This statement can be simple or compound. It simply reverses the truth value of any statement in front of which it appears. The logical negation symbol ¬ or ~ is one of the statement connectives or operators that can be used to form new compound statements from two or more statements. Thus, one might say, "Consider any statement, p" or "Suppose that a pair of statements, p and q, are both true." ![]() Lowercase letters of the alphabet, beginning with p, are used as statement variables. Thus, A, B and C can be used to represent the previous statements: Therefore, specific individual statements are represented using capital letters as statement constants. However, to express the logical relationships between such statements, it becomes cumbersome to write out the entire sentence at every occurrence of each statement. In ordinary, everyday language, statements can be conveyed by complete declarative sentences, such as the following: Compound statements and the logical negation symbol The option for using either symbol depends on the user's preference or the context to denote negation. Since the ~ and ¬ symbols can be used interchangeably, the above statement can also be represented logically as ~(A V B). ¬(A V B): Neither the sky is blue nor is the grass green The rules for using the logical negation symbol become more complicated when the symbol appears in complex statements. ¬A: The sky is not blue, or it is not true that the sky is blue ![]() However, its simplest use is with a single sentence. The symbol ¬ is often found within or preceding complex logical statements. Thus, if a statement is represented as A, then ¬A is the logical opposite or negation of A. It simply reverses the truth value of a given statement. The negation symbol is a unary logical operator.
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