![]() The conjunction of P and Q is written P ∧ Q, and expresses that each are true. Conjunction is a truth-functional connective which forms a proposition out of two simpler propositions, for example, P and Q.¬¬ P always has the same truth-value as P. In the example above, ¬ P expresses that it is not raining outside, or by a more standard reading: 'It is not the case that it is raining outside.' When P is true, ¬ P is false and when P is false, ¬ P is true. ![]() ¬ P represents the negation of P, which can be thought of as the denial of P. ![]() We then define truth-functional operators, beginning with negation.This will be true ( P) if it is raining outside and false otherwise ( ¬ P). For example, let P be the proposition that it is raining outside. All propositions require exactly one of two truth-values: true or false. Any given proposition may be represented with a letter called a 'propositional constant', analogous to representing a number by a letter in mathematics, for instance, a = 5.
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