MAT 142 Lecture Video Series. Symbolic Logic Objectives Determine if a sentence or question is a statement or not. Write a sentence that represents the.

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Presentation transcript:

MAT 142 Lecture Video Series

Symbolic Logic

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.

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 false a 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. 2. Solve the equation 2x + 5 = x = 0 has no solution.

Negation: Conjunction: Disjunction: Conditional: denial of a statement (symbol: ~) and (symbol: ^ ) Connectives or – 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 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.

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.

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.

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.

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.

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.

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