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Section 3.2

Section 3.2. Truth Tables for Negation, Conjunction, Disjunction. Purpose of Truth Tables. The purpose of a truth table is to list all the possible truth values of a statement. We use all the possible combinations of True/False for the letters in the statement: p, q, r. Negation Truth Table.

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Section 3.2

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  1. Section 3.2 Truth Tables for Negation, Conjunction, Disjunction

  2. Purpose of Truth Tables • The purpose of a truth table is to list all the possible truth values of a statement. • We use all the possible combinations of True/False for the letters in the statement: p, q, r

  3. Negation Truth Table • ~p • One letter, truth table has 2 rows

  4. Conjunction Truth Table • Truth value of the conjunction p Λ q • 2 letters = 4 rows

  5. Getting the Truth Table Started • The p rows alternate truth values 2 at a time, since 2 is half of 4 • The q rows alternate truth values 1 at a time, since 1 is half of 2

  6. Conjunction Truth Table • p Λ q is true only when both p and q are true. • Conjunction is usually false.

  7. Disjunction Truth Table

  8. Truth Tables • Example: Truth value of the conjunction p Λ ~q

  9. Truth Tables • Example: Truth value of the conjunction p Λ ~q

  10. Truth Tables • Example: Truth value of the conjunction p Λ ~q

  11. Truth Tables with Three Letters, Comma = Parentheses 3 statements: p, q, r p: You must get up early . q: You must stay up late. r: You must eat a good breakfast. “You must get up early or you must not stay up late, and you must eat a good breakfast.” (p v ~ q) Λ r

  12. Truth Tables with Three Letters • 3 letters require 8 rows in the truth table:

  13. Truth Table for (p v ~ q) Λ r

  14. Truth Table for (p v ~ q) Λ r

  15. Truth Table for (p v ~ q) Λ r

  16. Truth Table for (p v ~ q) Λ r

  17. Truth Tables are not required for known truth values When truth values of statements are known: 12 is less than 13 or 12 is equal to 13. T V F T 6 is an even number and 6 is divisible by 3. T Λ T T

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