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MAT 142 Lecture Video Series

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Symbolic Logic

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Objectives 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.

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Vocabulary Statement Compound statement Negation Conjunction Disjunction (inclusive or) Conditional (implication) Hypothesis (premise) Conclusion

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Statement: Compound statement: a statement is a sentence that is either true or false a statement that contains one or more simpler statement (not, and, or, if... then, only if, if and only if)

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Determine which of the following are statements. 2. Solve the equation 2x + 5 = 3. 3. x 2 + 1 = 0 has no solution.

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Negation: Conjunction: Disjunction: Conditional: denial of a statement (symbol: ~) and (symbol: ^ ) Connectives or – inclusive or (symbol: V) if..., then (symbol: )

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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.

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Negation Summary StatementNegation Some 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.

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Using 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. 1.The car is red, goes 140 mph, and does not cost $40,000.

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Using 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. 2.If the car does not cost $40,000, it does not go 140 mph.

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Using 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. 3.The car is red and it does not go 140 mph or cost $40,000.

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Using 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. 4.All red cars go 140 mph.

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Using 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.

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Creator and Producer Elizabeth Jones for The School of Mathematical and Statistical Sciences at Arizona State University Videographer Mike Jones ©2009 Elizabeth Jones and School of Mathematical and Statistical Sciences at Arizona State University

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Logic Disjunction A disjunction is a compound statement formed by combining two simple sentences using the word “OR”. A disjunction is true when at.

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