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AND. Chapter 3. Logic. WHAT YOU WILL LEARN. • Statements, quantifiers, and compound statements • Statements involving the words not , and , or , if… then… , and if and only if

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  1. AND

  2. Chapter 3 Logic

  3. WHAT YOU WILL LEARN • Statements, quantifiers, and compound statements • Statements involving the words not, and, or, if… then…, and if and only if • Truth tables for negations, conjunctions, disjunctions, conditional statements, and biconditional statements • Self-contradictions, tautologies, and implications

  4. WHAT YOU WILL LEARN • Equivalent statements, De Morgan’s law, and variations of conditional statements • Symbolic arguments and standard forms of arguments • Euler diagrams and syllogistic arguments • Using logic to analyze switching circuits

  5. Section 3 Truth Tables for theConditional and Biconditional

  6. p q Case 1 T T T Case 2 T F F Case 3 F T T Case 4 F F T Conditional The conditional statementpgqis true in every case except when p is a true statement and q is a false statement.

  7. p q (p q) (q p) case 1 T T T T T T T T T case 2 T F T F F F F T T case 3 F T F T T F T F F case 4 F F F T F T F T F order of steps 1 3 2 7 4 6 5 Biconditional The biconditional statement, p↔q means that p g q and qgp or, symbolically (pgq) (qgp).

  8. Example: Truth Table with a Conditional Construct a truth table for ~p g~q. Solution: Construct standard four case truth table. Then fill-in the table in order, as follows: T T F F T F T F F F T T T T F T F T F T 1 3 2 It’s a conditional, the answer lies under the g.

  9. Tautology • A tautology is a compound statement that is always true. • When every truth value in the answer column of the truth table is true, the statement is a tautology.

  10. Self-Contradiction • A self-contradiction is a compound statement that is always false. • When every truth value in the answer column of the truth table is false, then the statement is a self-contradiction.

  11. Implication • An implication is a conditional statement that is a tautology. • The consequent will be true whenever the antecedent is true.

  12. CourseSmart Page 133

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