Wetzel                                                                                                             

Math 122

Test #5

Read each problem carefully and completely answer each question.

Write the symbol for each term in the space provided.

1.)  _________            Conjunction

2.)  _________            Negation

3.)  _________            Bi-Conditional

4.)  _________            Negation

Given the following statements, write Conditional, Inverse, Converse, or Contra-positive in the space provided.

                        p:  I will wear a coat today.

                        q:  I will not be cold.

5.)  ______________  If I wear a coat today, I will not be cold.

6.)  ______________  If I am cold, I did not were a coat today.

7.)  ______________  If I am not cold, I wore a coat today.

8.)  ______________  If I do not wear a coat today, I will be cold.

True or False.  Determine if the following is a bi-conditional statement.

9.)  __________          If you run a 5 minute mile, then you are on the cross county team.

                                                (hint: not all team members can run a 5 minute mile)

10.)  _________          If 95% of the class fill out the course evaluation, then everybody                                                will receive two bonus points on the final exam.

Identify the following arguments as Law of Detachment, Syllogism, Disjunctive Syllogism, or Indirect Reasoning.

11.)  _________­­­­______          If I trim the hedges, then I may go to the movies.  I                                                                    trimmed the hedges.     

                        Conclusion:       I may go to the movies.

12.)  _______________          You will enjoy the book or you will enjoy the movie                                                      version.  You did not enjoy the book.

                        Conclusion:       You enjoyed the movie version.

13.)  _______________          If rain is in the forecast, then I will take my umbrella.  I did                                             not take my umbrella.

                        Conclusion:       Rain was not in the forecast.

14.)  Two major discount stores, A-mart and B-mart, compete for the business of the same customer base.  A-mart has 55% of the business and B-mart has 45% of the business.  Both companies are considering building new superstores to increase their market share.  If both build, or neither builds, they expect their market share to remain the same.  If A-mart builds and B-mart doesn’t , A-mart’s share increases to 65%.  If B-mart builds and A-mart doesn’t, then A-mart’s share drops to 50%.  The follow matrix illustrates this.

                                                     B-mart

                                                         B    NB

                           A-mart         

            a.)  Determine the value of the game, if it exists.

            b.)  Find the saddle point, if it exists.

            c.)  Explain the strategies A-mart and B-mart should take.