1b-Logic Tables and Laws.pdf - Propositional Logic...

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Fall 2019 - W. SchnyderDiscrete and Data StructuresLesson 1b - Logic1Fall 2019 - W. SchnyderPropositional Logic2Examples.2 + 3 = 6propositionfalseIt rained yesterdaypropositiontrueGive me money!no propositionThe number of hairs on Alice'shead is evenpropositiontrue or false, butno time to countDid she miss the bus?no propositionThis sentence is falseno propositionDefinition.AProposition(orStatement) is an assertion that is eithertrueorfalse.Fall 2019 - W. SchnyderPropositional Logic3Examples.True or False?NOT2 < 6False2 < 6AND7 < 5False9 < 7OR3 < 8TrueDefinition.Acompoundproposition is one that is obtained bycombination of other propositions. Asimpleproposition is onethat is not compound.Fall 2019 - W. SchnyderPropositional Logic4Propositional logic is concerned with how propositions are combinedusingoperators(also calledconnectives).OperatorSymbolFormMeaningANDconjunctionpqtrue exactly whenbothpand q are trueORdisjunctionpqtrue exactly whenat leastone ofp and q is trueNOTnegation¬¬ ptrue if p is false, andfalse if p is true.Acompoundproposition is one that is obtained by combination ofother propositions. Asimpleproposition is one that is not compound.Propositional LogicExercise.Letpbe"Fred is quick"andqbe"George is quick"Write the following statements in symbolic form.(a) Fred is quick and George is slowExercise.Suppose that Fred and George are both quick. Is any of thestatements (a) - (e) true?Exercise.The following statements are compound. Assign lettersto their simple components and write the statements in symbolicform..qqqqPropositional Logicq¬q¬q
Fall 2019 - W. Schnyder5Fall 2019 - W. Schnyder6
Fall 2019 - W. SchnyderPropositional Logic7Writing statement forms anduse of parentheses.Negation symbol¬binds strongest¬ pqmeans(¬ p)qand doesn’t mean¬ (pq)Symbolsandbind equallypqris ambiguous.

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Logic, Logical connective, Must P, W Schnyder

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