1. Truth Tables for Negation, Conjunction, and Disjunction

2.  Use the definitions of negation, conjunction, and disjunction.  Construct truth tables.  Determine the truth values of a compound statement for a specific case.

3.  In 2006, USA Today analyzed patterns in the deaths of four- year college students since January 2000. Their most dominant finding was the freshmen emerged as the class most likely to make a fatal mistake. Freshman accounted for more than 1/3 of all undergraduate deaths, even though they made up only 24% of the population enrolled in 4-year institutions.  In this section, you will work with 2 circle graphs based on data from the USA Today study. By determining when statements involving negation, ~ (not), conjunction, (and), and disjunction, (or), are true and when they are false, you will be able to draw conclusions from the data. Classifying a statement as true or false is called assigning a truth value to the statement.

4.  The negation of a true statement is a false statement, and the negation of a false statement is a true statement. We can express this in a table where T represents true and F represents false. p~p TF FT

5.  A friend tells you, “I visited London and I visited Paris.” In order to understand the truth values for this statement we will break it down into its two simple statements.  p: I visited London.  q: I visited Paris.  There are 4 possible cases to consider.

6.  4 Cases:  A conjunction statement is true only when both simple statements are true. pqp q TTT TFF FTF FFF

7.  Now your friend states, “I will visit London or I will visit Paris.”  p: I will visit London.  q: I will visit Paris.  There are 4 possible cases here to consider also.

8.  4 Cases:  A disjunction statement is false only when both component statements are false. pqp q TTT TFT FTT FFF

9.  If you learn the truth table for and and or by remembering the one different line in each table, it will help you do logic calculations more quickly.

10.  Determine the truth value for each statement.  p: 4 + 6 = 10  q: 5 X 8 = 80  ~p

11.  Determine the truth value for each statement.  p: 4 + 6 = 10  q: 5 X 8 = 80  q p

12.  Determine the truth value for each statement.  p: 4 + 6 = 10  q: 5 X 8 = 80  p ~q

13.  Determine the truth value for each statement.  p: 4 + 6 = 10  q: 5 X 8 = 80  ~q ~p

14.  If p represents a true statement and q represents a false statement, what is the truth value of each statement?  p q

15.  If p represents a true statement and q represents a false statement, what is the truth value of each statement?  p q

16.  If p represents a true statement and q represents a false statement, what is the truth value of each statement?  (~p) q

17.  If p represents a true statement and q represents a false statement, what is the truth value of each statement?  ~(p ~q)

18.  Use numbers to specify the order in which you would perform the logical operations for each statement.  (~p q) ~p

19.  Use numbers to specify the order in which you would perform the logical operations for each statement.  p ~ (q ~p) ~q

20.  Classwork:  TB pg. 98/1 – 12 All ▪ Remember you must write the problems and show ALL work to receive credit for the assignment.

21. Section 2.3 Continued

22.  Construct a truth table.  (~p) q

23.  Construct a truth table.  ~(p ~q)

24.  Construct a truth table.  (p q) ~p

25.  Construct a truth table.  (p ~q) (~p q)

26.  Construct a truth table.  (p ~q) (~p q)

27.  Some truth tables have 3 simple statements. In this situation, you would have 8 cases. pqr TTT TTF TFT TFF FTT FTF FFT FFF

28.  p (~q r)

29.  ~(p q) ~r

30.  ~(p ~q) ~r

31.  Logically Equivalent – two statements that have the same variable, and when their truth tables are computed, the final columns are identical.

32.  Determine if the two compound statements are logically equivalent.  ~(p ~q) ~ (p q) p (p q)

33.  Determine if the two compound statements are logically equivalent.  ~(p ~q) ~ (p q) (~p q) (~p ~q)

34.  Classwork:  TB pg. 98/30 – 40 Even, and 60 – 66 Even ▪ Remember you must write the problem and show ALL work to receive credit for this assignment. ▪ NOTE: If your truth tables are not complete, then your answer is wrong.