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Symbolic Logic

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

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Symbolic Logic

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  1. Symbolic Logic

  2. 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.

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

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

  5. Determine which of the following are statements. 2. Solve the equation 2x + 5 = 3. 3. x2 + 1 = 0 has no solution.

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

  7. Write the statement that represents the negation: • His car is not new. • Some buildings are earthquakeproof. • All children eat candy. • I never cry in a movie theater.

  8. Negation Summary

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

  10. 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. • If the car does not cost $40,000, it does not go 140 mph.

  11. 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. • The car is red and it does not go 140 mps or cost $40,000.

  12. 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. • All red cars go 140 mph.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

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