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4. Contents Lesson 2-2Logic OBJECTIVE: To construct truth tables (2.8.11Q) (M8.D.1.1)

5. Lesson 2 Contents Example 1Truth Values of Conjunctions Example 2Truth Values of Disjunctions Example 3Use Venn Diagrams Example 4Construct Truth Tables

6. Example 2-4a Step 1 Make columns with the headings p, q, ~p, and ~p Construct a truth table for. ~p ~p~p q p

7. Example 2-4b Step 2 List the possible combinations of truth values for p and q. Construct a truth table for. FF TF FT TT ~p ~p~p qp

8. Example 2-4c Step 3 Use the truth values of p to determine the truth values of ~p. Construct a truth table for. TFF TTF FFT FTT ~p ~p~p qp

9. Example 2-4d Step 4 Use the truth values for ~p and q to write the truth values for ~p  q. Answer: Construct a truth table for. TTFF TTTF FFFT TFTT ~p ~p~p qp

10. Example 2-4f p  (~q  r)~q  r~q  r ~qrqp Step 1 Make columns with the headings p, q, r, ~q, ~q  r, and p  (~q  r). Construct a truth table for.

11. Example 2-4g Step 2 List the possible combinations of truth values for p, q, and r. Construct a truth table for. FFF p  (~q  r)~q  r~q  r ~q F T T F F T T r TF TT FT TF FF FT TT qp

12. Example 2-4h Step 3 Use the truth values of q to determine the truth values of ~q. Construct a truth table for. TFFF p  (~q  r)~q  r~q  r F T F T F T F ~q F T T F F T T r TF TT FT TF FF FT TT qp

13. Example 2-4i Step 4 Use the truth values for ~q and r to write the truth values for ~q  r. Construct a truth table for. FTFFF p  (~q  r) F T F F F T F ~q  r~q  r F T F T F T F ~q F T T F F T T r TF TT FT TF FF FT TT qp

14. Example 2-4j Step 5 Use the truth values for p and ~q  r to write the truth values for p  (~q  r). Answer: Construct a truth table for. FFTFFF F T F T T T T p  (~q  r) F T F F F T F ~q  r~q  r F T F T F T F ~q F T T F F T T r TF TT FT TF FF FT TT qp

15. Example 2-4l Construct a truth table for (p  q)  ~r. (p  q)  ~rp  qp  q ~rrqp Step 1 Make columns with the headings p, q, r, ~r, p  q, and (p  q)  ~r.

16. Example 2-4m Step 2 List the possible combinations of truth values for p, q, and r. FFF (p  q)  ~rp  qp  q ~r F T T F F T T r TF TT FT TF FF FT TT qp Construct a truth table for (p  q)  ~r.

17. Example 2-4n Step 3 Use the truth values of r to determine the truth values of ~r. Construct a truth table for (p  q)  ~r. TFFF (p  q)  ~rp  qp  q T F F T T F F ~r F T T F F T T r TF TT FT TF FF FT TT qp

18. Example 2-4o Step 4 Use the truth values for p and q to write the truth values for p  q. Construct a truth table for (p  q)  ~r. FTFFF (p  q)  ~r T F T T T T T p  qp  q T F F T T F F ~r F T T F F T T r TF TT FT TF FF FT TT qp

19. Example 2-4p Step 5 Use the truth values for p  q and ~r to write the truth values for (p  q)  ~r. Answer: Construct a truth table for (p  q)  ~r. FFTFFF F F T F T F T (p  q)  ~r T F T T T T T p  qp  q T F F T T F F ~r F T T F F T T r TF TT FT TF FF FT TT qp

20. Example 2-4r Construct a truth table for the following compound statement. a. FFFFFF F F T F T F T F F T F F F T F F F F T F T TFF F T F F T T r TT FT TF TF FT TT qp Answer:

21. Example 2-4s b. Answer: FFFFFF T F T F T T T T T T F T T T T F T T T T T TFF F T F F T T r TT FT TF TF FT TT qp Construct a truth table for the following compound statement.

22. Example 2-4t c. Answer: FFFFFF T F T T T T T F F T F F F T T F T T T T T TFF F T F F T T r TT FT TF TF FT TT qp Construct a truth table for the following compound statement.

23. Review Construct a truth table for p^q. pqp^q TTT TFF FTF FFF

24. End of Lesson 2

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