1. Chapter 3 section 1

2.  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.  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.  1. Statement  2. Not a statement  3. statement

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

6.  When an idea is not true. Notation symbol is ~

7. 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.  Expresses the idea of and. Symbol notation is

9.  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.  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.  Conveys the notion of or. Notation is V

12. 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.  Expresses the notation of if…then.  Notation

14. 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 :

16. 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.

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

19.  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

21.  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.

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

27.  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.

29.  Thanks