MAT 142 Lecture Video Series Symbolic Logic Objectives

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: a statement is a sentence that is either true or false • Compound statement: 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 2 x + 5 = 3. 3. x 2 + 1 = 0 has no solution.

• Negation: Connectives denial of a statement (symbol: ~) • Conjunction: and (symbol: ^) • Disjunction: or – inclusive or (symbol: V) • Conditional: 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 Statement Negation Some p are q. No p are q. All p are q. Some p are not q. No 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.

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.

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.

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.

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