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Unformatted text preview: Notes 6.2 Truth Functions The truth value of a compound proposition expressed in terms of one or more logical operators is said to be a function of the truth value of the components. That is, the truth value of an entire compound proposition is completely determined by the truth value of the components. Thus, you can represent the truth value of propositions by making a truth table . So, here’s the one for negation: Negation p ~p T F F T Clearly, where p is true, then ~p has to be false. Where ~p is false, then p is true. (The p on either side stands for an ENTIRE proposition. These could be anything like A, A v B, or ~[(C v A) · (A · E)]. The point is simply that, where a statement is negated, it will have the opposite truth value of the proposition it’s negating.) _______________________________________________________________________ _______________________________________________________________________ __ The definition of the operator for conjunction is show by determining the truth values for either conjunct: Conjunction p q p · q T T T T F F F T F F F F So we see that p · q is only ever true if both conjuncts are true—and false in all other cases. This makes sense in normal English cases, too. Take the following statements: Ferrari and Maserati make sports cars F · M Ferrari and GMC make sports cars F · G GMC and Jeep make sports cars G · J The first sentence, AS A WHOLE, is true, because both conjuncts are true. The latter two are both false because at least one of the conjuncts is false. _______________________________________________________________________...
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This note was uploaded on 05/04/2008 for the course PHIL 2203 taught by Professor Barrett during the Spring '08 term at Arkansas.
- Spring '08