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logic1 - Some Useful Logic Part 1 Math 8 2009 Chris Lyons...

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Unformatted text preview: Some Useful Logic: Part 1 Math 8 2009, Chris Lyons Logical statements and negation • Let’s denote a true-or-false statement using letters P , Q , R , etc. For example, we could have the statement P be P : “I’m eating an apple.” • We say that a statement P is equivalent to another statement Q if P is true exactly when Q is true (and therefore if P is false exactly when Q is false). • If we have a statement P , then ¬ P will denote the logically opposite statement, which we call its negation . In other words, P is true exactly when ¬ P is false (and therefore P is false exactly when ¬ P is true). In the example above, we have ¬ P : “I’m not eating an apple.” • The statement ¬¬ P is equivalent to P . The AND and OR operations • Here are two ways to join a pair of statements into one new statement, using the AND and OR operations. For instance, suppose we have P : “I’m eating an apple.” Q : “I’m watching TV.” • Define P AND Q as the statement which is true exactly when both P and Q are true, and is false otherwise. Using our examples, we haveotherwise....
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This note was uploaded on 07/19/2010 for the course MA 8 taught by Professor Vuletic,m during the Fall '08 term at Caltech.

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logic1 - Some Useful Logic Part 1 Math 8 2009 Chris Lyons...

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