1. Truth Values and Connectives
Lesson 5.3
Truth Values and Connectives pp

2. Objectives:
1. To define and apply the logic connectives disjunctions and conjunction.
2. To identify the truth values of the connectives and set them down in tabular form (truth table).
3. To use truth tables to establish the truth value of compound statements.

3. Truth tables provide a summary of the truth values for statements
Truth tables provide a summary of the truth values for statements. Truth tables use T for true and F for false. p ~p T F F T

4. Definition
A conjunction is a statement in which two statements, p and q, are connected by and. The notation for conjunction “p and q” is denoted p  q.

5. Truth table for a conjunction
p q p  q T T T T F F F T F F F F

6. Definition
A disjunction is a statement in which two statements, p and q, are connected by or. The notation for disjunction “p or q” is denoted p  q.

7. Truth table for a disjunction
p q p  q T F T T T F

8. EXAMPLE 1 Is this statement true or false?
“Mars is a planet, and the moon is green cheese.”
False; Because of the word and, it is a conjunction.

9. Truth table for a conjunction
p q p  q T T T T F F F T F F F F

10. You can make truth tables for more complicated expressions
You can make truth tables for more complicated expressions. First, decide how many combinations of true or false statements should be. If there are n statements then there are 2n rows in the truth table.

11. EXAMPLE 2 Give a truth table for (pr)(q~r).
Since there are 3 statements (p, q, & r), we will need 23 = 8 rows.

12. EXAMPLE 2 Give a truth table for (pr)(q~r).
p q r
(pr) r (qr) (pr)(qr)
T T T
T T F
T F T
T F F
F T T
F T F
F F T
F F F
T F F T
F T T T
F T F F
F F F F

13. Homework pp

14. ►A. Exercises
Tell whether the following statements are disjunctions or conjunctions and then tell whether they are true or false.
1. A spider is not an insect, or a
porpoise is not a fish.

15. ►A. Exercises
Tell whether the following statements are disjunctions or conjunctions and then tell whether they are true or false.
3. A stop sign is red, and a yield sign is blue.

16. ►A. Exercises
Tell whether the following statements are disjunctions or conjunctions and then tell whether they are true or false.
9. 9  9 and 2  5

17. ►B. Exercises
Tell whether the following statements are disjunctions or conjunctions and then tell whether they are true or false.
11. Orange is made from green and yellow, while lavender is made from red and blue.

18. ►B. Exercises
Tell whether the following statements are disjunctions or conjunctions and then tell whether they are true or false.
13. Five plus three is eight, but five times
three is fifteen.

19. ►B. Exercises
Make truth tables for each compound statement below. Be sure to list all possible combinations of T and F in an orderly manner.
15. p  ~p
p ~p p  ~p

20. ►B. Exercises
Make truth tables for each compound statement below. Be sure to list all possible combinations of T and F in an orderly manner.
15. p  ~p
p ~p p  ~p T F F F T F

21. ►B. Exercises
Make truth tables for each compound statement below. Be sure to list all possible combinations of T and F in an orderly manner.
17. (a  b)  ~a

22. ►B. Exercises
17. (a  b)  ~a
a b (a  b) ~a (a  b)  ~a

23. T T T F T T F F F F F T F T T F F F T T ►B. Exercises 17. (a  b)  ~a
a b (a  b) ~a (a  b)  ~a T T T F T T F F F F F T F T T F F F T T

24. ►B. Exercises
Make truth tables for each compound statement below. Be sure to list all possible combinations of T and F in an orderly manner.
19. p  (q  r)

25. ►B. Exercises
19. p  (q  r)
p q r q  r p  (q  r)

26. ►B. Exercises 19. p  (q  r) p q r q  r p  (q  r) T T T T T T T F

27. ■ Cumulative Review
True/False
23. A square is a rhombus, and a square is a rectangle.

28. ■ Cumulative Review 24. A prism is a cone, and a prism is a cylinder.
True/False
24. A prism is a cone, and a prism is a cylinder.

29. ■ Cumulative Review
True/False
25. A polygon is both a simple curve and a closed curve.

30. ■ Cumulative Review
True/False
26. A tetrahedron has four edges, or it has four vertices.

31. ■ Cumulative Review
True/False
27. An octahedron has eight edges, or it has eight vertices.