# DARTMOUTH COSC 030 - 03logic (9 pages)

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## 03logic

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- Pages:
- 9
- School:
- Dartmouth College
- Course:
- Cosc 030 - Discrete Math Computer Sci

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Proposition A declarative sentence that is either true or false but not both Examples CS 30 Discrete Mathematics Amit Chakrabarti Logic and Logical Notation Compound Proposition One that can be broken down into more primitive propositions E g If it is sunny outside then I walk to work otherwise I drive and if it is raining then I carry my umbrella This consists of several primitive propositions p It is sunny outside r I drive t I carry my umbrella q I walk to work s It is raining Connectives if then otherwise and CS 30 is a required course for the CS major The population of New York City is more than 8 000 000 Pigs can Jly Non examples What a beautiful evening Do your homework Compound Proposition If it is sunny outside then I walk to work otherwise I drive and if it is raining then I carry my umbrella p It is sunny outside r I drive t I carry my umbrella q I walk to work s It is raining If p then q otherwise r and if s then t If p then q and if not p then r and if s then t p implies q and not p implies r and s implies t Logical Connectives Compound Proposition in Symbols Used to form compound propositions from primitive ones English name Math name Symbol C C Java and conjuction or disjunction not negation or but not both xor none if then implication none if only if equivalence none If it is sunny outside then I walk to work otherwise I drive and if it is raining then I carry my umbrella p It is sunny outside r I drive t I carry my umbrella q I walk to work s It is raining p implies q and not p implies r and s implies t p q p r s t Defining a Logical Connective How to deJine p q Consider the four possibilities p is true q is true p is true q is false p is false q is true p is false q is false In each case specify the truth value of p q p q p q true true true true false false false true false false false false Truth Table Pondering Implication p q p q T T T T F F F T F F F F s It is raining t I carry my umbrella s t Think of the implication as a promise or a contract if s then I guarantee that t In which of the following situations can I say that I have stood by my contract Situation 1 It was raining and I carried my umbrella s is true t is true Pondering Implication Pondering Implication s It is raining t I carry my umbrella s t Think of the implication as a promise or a contract if s then I guarantee that t In which of the following situations

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