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Chapter 2.2

Chapter 2.2. Logic: Introduce use of Venn Diagrams and Truth Tables. Logic Statements - process. p: The sky is blue. q: The grass is green. r: The moon is made of blue cheese. Negations. ~p: The sky is NOT blue. ~q: The grass is NOT green.

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Chapter 2.2

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  1. Chapter 2.2 Logic: Introduce use of Venn Diagrams and Truth Tables

  2. Logic Statements - process p: The sky is blue. q: The grass is green. r: The moon is made of blue cheese. Negations • ~p: The sky is NOTblue. • ~q: The grassis NOT green. • ~r: The moon is NOT made of blue cheese. • ~p is true, when p is false and ~p is false, when p is true.

  3. Statements Compound Statements p: The sky is blue. q: The grass is green. r: The moon is made of blue cheese. • p and q • The sky is blue and the grass is green. • p  q • q  r • The grass is green and the moon is made of blue cheese • Only true if both are true

  4. p: The sky is blue. q: The grass is green. r: The moon is made of blue cheese. Disjunctions • p or q • The sky is blue or the grass is green. • p  q • q  r • The grass is green or the moon is made of blue cheese. True if at least one is true

  5. Truth Values Conjunctions  Disjunctions  p or q pq, True r  p True p and not r p  ~ r, True ~r  q False p: January 1 is the first day of the year q: -5 +11 = -6 r: A triangle has three sides • p and q • pq, False • r  p • True • p and not r • p  ~ r, false • ~q  r • True

  6. Truth Tables Both have to be true for a conjunction to be true Negation Conjunction Disjunction Both have to be false for disjunction to be false

  7. Build a Truth Table Process p  ~ q • Build Columns • Each variable • Any negations • Conjunction/Disjunction • List possible combinations of variables • Determine values for negations (if any) • Determine value for Conjunction/Disjunctions

  8. Example 3 Construct Truth Tables B.Construct a truth table for p (~q  r). Step 1 Make columns with the headings p, q, r, ~q, ~qr, and p  (~q  r).

  9. Construct Truth Tables B.Construct a truth table for p (~q  r). Step 2 List the possible combinations of truth values for p, q, and r.

  10. Construct Truth Tables B.Construct a truth table for p (~q  r). Step 3 Use the truth values of q to determine the truth values of ~q.

  11. Construct Truth Tables B.Construct a truth table for p (~q  r). Step 4 Use the truth values for ~q and r to write the truth values for ~q r.

  12. Construct Truth Tables B.Construct a truth table for p (~q  r). Step 5 Use the truth values for ~q rand p to write the truth values for p (~q r). Answer:

  13. Conjunction or Disjunction? Venn Diagram Cities in Tennessee US State Capitals Nashville

  14. Venn Diagram q:Girls Soccer 21 p: Cheerleaders 20 6 r: Girls Basketball 15 0 2 0

  15. Practice Assignment • Page 102; 32 - 62 Even

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