Symbolic LogicObjectivesVocabularySlide 4Determine which of the following are statements.Slide 6Write the statement that represents the negation:Negation SummaryUsing the symbolic representations p: The car costs $40,000. q: The car goes 140 miles per hour. r: The car is red. express the following compound statements in symbolic form.Slide 10Slide 11Slide 12Using the symbolic representations p: I am an environmentalist. q: I recycle my aluminum cans. r: I recycle my newspapers. express the following compound statements in symbolic form.Slide 14Slide 15Slide 16Symbolic LogicObjectives•Determine if a sentence or question is a statement or not. •Write a sentence that represents the negation of a given statement. •Rewrite a statement in symbolic form (defining the symbols used). •Rewrite a symbolic statement in word form.Vocabulary•Statement•Compound statement•Negation•Conjunction•Disjunction (inclusive or)•Conditional (implication)•Hypothesis (premise)•Conclusion•Statement:•Compound statement:a statement is a sentence that is either true or falsea statement that contains one or more simpler statement(not, and, or, if . . . then, only if, if and only if)Determine which of the following are statements.)1)(1(1.42 xxx653.1 2. Solve the equation 2x + 5 = 3.3. x2 + 1 = 0 has no solution.number?rationala2Is.5•Negation:•Conjunction:•Disjunction:•Conditional:denial of a statement (symbol: ~)and (symbol: ^)Connectivesor – inclusive or (symbol: V)if . . ., then (symbol: →)Write the statement that represents the negation:1. His car is not new.2. Some buildings are earthquakeproof.3. All children eat candy.4. I never cry in a movie theater.Negation SummaryStatement NegationSome p are q. No p are q.All p are q. Some p are not q.No p are q. Some p are q.Some p are not q. All p are q.Using the symbolic representationsp: The car costs $40,000.q: The car goes 140 miles per hour.r: The car is red.express the following compound statements in symbolic form.1.The car is red, goes 140 mph, and does not cost $40,000.Using the symbolic representationsp: The car costs $40,000.q: The car goes 140 miles per hour.r: The car is red.express the following compound statements in symbolic form.2.If the car does not cost $40,000, it does not go 140 mph.Using the symbolic representationsp: The car costs $40,000.q: The car goes 140 miles per hour.r: The car is red.express the following compound statements in symbolic form.3.The car is red and it does not go 140 mps or cost $40,000.Using the symbolic representationsp: The car costs $40,000.q: The car goes 140 miles per hour.r: The car is red.express the following compound statements in symbolic form.4.All red cars go 140 mph.Using the symbolic representationsp: I am an environmentalist.q: I recycle my aluminum cans.r: I recycle my newspapers.express the following compound statements in symbolic form. prq .1Using the symbolic representationsp: I am an environmentalist.q: I recycle my aluminum cans.r: I recycle my newspapers.express the following compound statements in symbolic form.)(~.2 rqp Using the symbolic representationsp: I am an environmentalist.q: I recycle my aluminum cans.r: I recycle my newspapers.express the following compound statements in symbolic form.prq ~)(.3 Using the symbolic representationsp: I am an environmentalist.q: I recycle my aluminum cans.r: I recycle my newspapers.express the following compound statements in symbolic form.pqr ~)~(.4
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