Statements, connectives, and Quantifiers.

1. Statements, connectives, and Quantifiers. Chapter 3 section 1

2. Logic • A statement • Is a declarative sentence that is either true or false. (using lower case letters p, q, r …) • 2 Types of statement • Simple – contains a single idea. • Compound – contains several ideas.

3. Examples Determine which sentence are statements. 1. More than half the households in the country have digital cameras. 2. Come skiing with me this weekend in Tahoe. 3. You will be a millionaire by the time you are 30.

4. Solutions 1. Statement 2. Not a statement 3. statement

5. Example AIDS is a leading killer of men. Statement You’re hired! Not a statement

6. Negation • When an idea is not true. • Notation symbol is ~

7. Try this! • Example • p: The optical disk drive is included in the price of the computer. • Write the sentence using negation. • The optical disk drive is not included in the price of the computer. • Write the using symbolic notation. • ~p

8. Conjunction • Expresses the idea of and. • Symbol notation is

9. Try this! p = the tenant pays utilities, d = $150 deposit is required Write “It is not true that: the tenant pays utilities and a $150 deposit is required” symbolically. I can rewrite the statement as follows ~(p ^ d)

10. Try the following • Write the statement • ~p ^ ~d • The tenant does not pay utilities and does not require a $150 deposit • p ^ d • The tenant pays utilities and requires a $150 deposit.

11. disjunction • Conveys the notion of or. • Notation is V

12. Example Consider the following statements: u: Urban sprawl will increase c: Commuting will be more difficult Write the statement symbolically Urban sprawl will not increase or commuting will be more difficult. (~u) V c It is not true that: urban sprawl will increase or commuting will be more difficult. ~(u V c)

13. Conditional Expresses the notation of if…then. Notation

14. Example c represents “clean your room” and p represents that you will be punished. Write the following in symbolic notation If you do not clean your room then you will be punished.

15. Solution Solution :

16. Try it. p = The Phillies win the world series and s = Susan will win an Emmy. If the Phillies do not win the world series, then Susan will not win an Emmy.

17. Solution

18. Biconditional Represents the idea of if and only if. Notation

19. Write the following statement in symbolic form p = polygon has three sides t = it is a triangle. 1. A polygon has three sides iff it is a triangle. s = the software can be returned b = the seal is broken 2. The software can be returned iff the seal is not broken

20. Solution

21. Write the following in symbolic notation r = The republicans will control congress t = taxes will be cut s= social programs will be increased 1) The republicans will control congress or social programs will not be increased.  2) The republicans will not control congress and the social programs will increase. 3) If social programs are not increased, then the republicans will not control congress or taxes will not be cut.

22. Solution

23. t= radial tires are included s= sunroof is extra w= power windows are optional 1. It is not true that the sunroof is extra and the redial tires are included. 2. If the sunroof is extra and the radial tires are included, then the power windows are not operational.

25. Try these questions. Identify each statement as simple or compound if the statement is compound, identify the connectives uesd. 1. 4. Alvaro likes opera. 2. LeBron or Kobe will lead the conference in scoring. 3. If you want to ride, you must be at least 48 inches tall and have no food, drinks, or Kryptonite.

26. Solutions 1. Simple 2. Compound; or 3. Compound; if…then, and, or

27. Write in symbolic form 1. Global warming will increase if and only if we do not develop alternative energy source. 2. If global warming does not increase then; Congress will not pass new energy legislation and we will not develop alternative energy source.

28. Solution

29. That is all Thanks