Finite Mathematics for the Managerial, Life, and Social Sciences
12th Edition
ISBN: 9781337405782
Author: Soo T. Tan
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter A.3, Problem 38E
To determine
(a)
To represent:
The statement “if the unemployment rate does not decrease, consumer confidence will not improve.” symbolically.
To determine
(b)
To represent:
The statement “Consumer confidence will improve if and only if the unemployment rate does not decrease.” symbolically.
To determine
(c)
To represent:
The statement “A decreasing unemployment rate is a sufficient condition for consumer confidence to improve.” symbolically.
To determine
(d)
To represent:
The statement “A decreasing unemployment rate is a necessary and sufficient condition for consumer confidence to improve.” symbolically.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Consider statements p and q.
p: More freshman chose to major in history than in nursing.
q: Math was chosen by the fewest number of freshmen.
2. Determine the validity of the following argument.
If the stock market rises, then the bond market will fall.
The bond market did not fall.
.. The stock market did not rise.
Let r represent "The stock market rises." Let f represent "The bond market will fall."
Formulate the following argument symbolically and determine whether each is
valid:
Let p: I study hard
q: I get an excellent grade
r: I get rich
1. If I study hard, then I get an excellent grade.
I study hard.
Therefore, I get an excellent grade.
2. If I study hard, then I get an excellent grade.
If I don't get rich, then I don't get an excellent grade.
Therefore, I get rich.
3. I study hard if and only if I get rich.
I get rich.
Therefore, I study hard.
4. If I study hard then I get an excellent grade or I get rich.
I don't get an excellent grade and I don't get rich.
Therefore, I don't study hard.
5. I get rich or I get and excellent grade.
I study hard.
Therefore, I don't get rich.
Chapter A Solutions
Finite Mathematics for the Managerial, Life, and Social Sciences
Ch. A.1 - In Exercises 114, determine whether the statement...Ch. A.1 - In Exercises 114, determine whether the statement...Ch. A.1 - Prob. 3ECh. A.1 - Prob. 4ECh. A.1 - Prob. 5ECh. A.1 - Prob. 6ECh. A.1 - Prob. 7ECh. A.1 - Prob. 8ECh. A.1 - Prob. 9ECh. A.1 - Prob. 10E
Ch. A.1 - Prob. 11ECh. A.1 - Prob. 12ECh. A.1 - Prob. 13ECh. A.1 - Prob. 14ECh. A.1 - Prob. 15ECh. A.1 - Prob. 16ECh. A.1 - Prob. 17ECh. A.1 - Prob. 18ECh. A.1 - Prob. 19ECh. A.1 - Prob. 20ECh. A.1 - Prob. 21ECh. A.1 - Prob. 22ECh. A.1 - Prob. 23ECh. A.1 - Prob. 24ECh. A.1 - Prob. 25ECh. A.1 - Prob. 26ECh. A.1 - Prob. 27ECh. A.1 - Prob. 28ECh. A.1 - Prob. 29ECh. A.1 - Let p and q denote the propositions p: The...Ch. A.1 - Prob. 31ECh. A.1 - Prob. 32ECh. A.1 - Prob. 33ECh. A.2 - Prob. 1ECh. A.2 - Prob. 2ECh. A.2 - Prob. 3ECh. A.2 - Prob. 4ECh. A.2 - In Exercises 1-18, construct a truth table for...Ch. A.2 - Prob. 6ECh. A.2 - Prob. 7ECh. A.2 - In Exercises 1-18, construct a truth table for...Ch. A.2 - Prob. 9ECh. A.2 - Prob. 10ECh. A.2 - Prob. 11ECh. A.2 - Prob. 12ECh. A.2 - Prob. 13ECh. A.2 - Prob. 14ECh. A.2 - Prob. 15ECh. A.2 - Prob. 16ECh. A.2 - Prob. 17ECh. A.2 - Prob. 18ECh. A.2 - If a compound proposition consists of the prime...Ch. A.3 - In Exercises 14, write the converse, the...Ch. A.3 - In Exercises 14, write the converse, the...Ch. A.3 - Prob. 3ECh. A.3 - Prob. 4ECh. A.3 - Prob. 5ECh. A.3 - In Exercises 5 and 6, refer to the following...Ch. A.3 - Prob. 7ECh. A.3 - Prob. 8ECh. A.3 - Prob. 9ECh. A.3 - Prob. 10ECh. A.3 - Prob. 11ECh. A.3 - Prob. 12ECh. A.3 - Prob. 13ECh. A.3 - Prob. 14ECh. A.3 - Prob. 15ECh. A.3 - Prob. 16ECh. A.3 - Prob. 17ECh. A.3 - Prob. 18ECh. A.3 - Prob. 19ECh. A.3 - Prob. 20ECh. A.3 - Prob. 21ECh. A.3 - Prob. 22ECh. A.3 - Prob. 23ECh. A.3 - Prob. 24ECh. A.3 - Prob. 25ECh. A.3 - Prob. 26ECh. A.3 - Prob. 27ECh. A.3 - Prob. 28ECh. A.3 - Prob. 29ECh. A.3 - Prob. 30ECh. A.3 - Prob. 31ECh. A.3 - Prob. 32ECh. A.3 - Prob. 33ECh. A.3 - Prob. 34ECh. A.3 - Prob. 35ECh. A.3 - Prob. 36ECh. A.3 - Prob. 37ECh. A.3 - Prob. 38ECh. A.4 - Prove the idempotent law for conjunction, ppp.Ch. A.4 - Prob. 2ECh. A.4 - Prove the associative law for conjunction,...Ch. A.4 - Prob. 4ECh. A.4 - Prove the commutative law for conjunction, pqqp.Ch. A.4 - Prob. 6ECh. A.4 - Prob. 7ECh. A.4 - Prob. 8ECh. A.4 - Prob. 9ECh. A.4 - Prob. 10ECh. A.4 - Prob. 11ECh. A.4 - Prob. 12ECh. A.4 - Prob. 13ECh. A.4 - Prob. 14ECh. A.4 - Prob. 15ECh. A.4 - Prob. 16ECh. A.4 - Prob. 17ECh. A.4 - In exercises 9-18, determine whether the statement...Ch. A.4 - Prob. 19ECh. A.4 - Prob. 20ECh. A.4 - In Exercises 21-26, use the laws of logic to prove...Ch. A.4 - Prob. 22ECh. A.4 - In Exercises 21-26, use the laws of logic to prove...Ch. A.4 - In Exercises 21-26, use the laws of logic to prove...Ch. A.4 - In Exercises 21-26, use the laws of logic to prove...Ch. A.4 - Prob. 26ECh. A.5 - Prob. 1ECh. A.5 - Prob. 2ECh. A.5 - Prob. 3ECh. A.5 - Prob. 4ECh. A.5 - Prob. 5ECh. A.5 - Prob. 6ECh. A.5 - Prob. 7ECh. A.5 - Prob. 8ECh. A.5 - Prob. 9ECh. A.5 - In Exercises 116, determine whether the argument...Ch. A.5 - Prob. 11ECh. A.5 - Prob. 12ECh. A.5 - Prob. 13ECh. A.5 - Prob. 14ECh. A.5 - Prob. 15ECh. A.5 - Prob. 16ECh. A.5 - In Exercises 17-22, represent the argument...Ch. A.5 - Prob. 18ECh. A.5 - In Exercises 17-22, represent the argument...Ch. A.5 - In Exercises 17-22, represent the argument...Ch. A.5 - In Exercises 17-22, represent the argument...Ch. A.5 - Prob. 22ECh. A.5 - Prob. 23ECh. A.5 - Prob. 24ECh. A.5 - Prob. 25ECh. A.6 - In Exercises 1-5, find a logic statement...Ch. A.6 - Prob. 2ECh. A.6 - Prob. 3ECh. A.6 - Prob. 4ECh. A.6 - Prob. 5ECh. A.6 - Prob. 6ECh. A.6 - Prob. 7ECh. A.6 - Prob. 8ECh. A.6 - Prob. 9ECh. A.6 - Prob. 10ECh. A.6 - Prob. 11ECh. A.6 - Prob. 12ECh. A.6 - Prob. 13ECh. A.6 - In Exercise 12-15, find a logic statement...Ch. A.6 - Prob. 15ECh. A.6 - Prob. 16E
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Complete the table by testing the validity of each argument using common patterns of reasoning All racers live dangerously. Gomer is a racer. Therefore, Gomer lives dangerously. 11. If you aren't polite, you won't be treated with respect. You aren't treated with respect. Therefore, you aren't polite. 12. If you are kind to a puppy, then he will be your friend. You weren't kind to that puppy. Hence, he isn't your friend. 13. If I don't pay my income taxes, then I file for an extension or I am a felon. I'm not a felon and I didn't file for an extension. Therefore, I paid my income taxes 14. I wash the dishes or I don't eat. I eat. Thus, I wash the dishes 15. If you play golf during a thunderstorm, you'll get hit by lightning. You didn't get hit by lightning. Therefore, you didn't play golf during a thunderstorm. 16. If an animal is a squid, then it has tentacles. If an animal is an octopus, then it has…arrow_forwardWhich of the statements mart and Lynn made are true ?arrow_forwardAfter the premiere of the new comedy Bumblebee, moviegoers we're asked in a quick poll whether they liked the movie. Out of 50 adults, all but 14 said they liked the movie, whereas out of 20 teenagers, all but 8 said they liked the movie. Fill in the blanks of the statement below to make the statement the most reasonable possible. At the movie premiere, _________ moviegoers liked the movie more because only _____% disliked the movie, whereas _____% of the ______ moviegoers disliked the movie.arrow_forward
- Write the contrapositive of the statement.If the magazine article is accurate, then stock prices are holding steady. If stock prices are not holding steady, then the magazine article is not accurate. If the magazine article is not accurate, then it is misleading. If stock prices are not holding steady, then the magazine article is accurate. If the magazine article is not accurate, then stock prices are not holding steady.arrow_forwardIdentify each situation as INDUCTUVE or DEDUCTIVE REASONING and provide explanation/ the reason why it is inductive or deductive reasoning. 1. Smith owns only blue pants and brown pants. Smith is wearing a pair of pants today. So, Smith is wearing either blue or brown pants today. January has been cold here in Siberia. Today is January 14, so it is going to be another cold day in Siberia. 2.arrow_forwardLet p and q represent the following statements. p: The taxes are high. q: The job pays well. Write the compound statement -p + ~q in words. Choose the correct answer below. O A. The taxes are not high if and only if the job does not pay well. O B. The job pays well if and only if the taxes are not high. O C. If the taxes are high, then the job does not pay well. D. If the taxes are high, then the job pays well.arrow_forward
- Identify each situation as INDUCTUVE or DEDUCTIVE REASONING and provide explanation/ the reason why it is inductive or deductive reasoning. Premise: All turtles have shells. Conclusion: I conclude that the animal in my bag has a shell. Premise: The animal I have captured is a turtle. Premise: Tonya is seen walking from her car to her home with a set of golf clubs. Conclusion: Tonya has bought the set of golf clubs for Jack. Premise: Tonya's husband Jeff loves golf and tomorrow is his birthday. Given: 5(x+2) = -3x - 6 ST 5 6. Prove: x = -27arrow_forward2). Write each symbolic statement in words. Use the variables m, n, and r as defined below. m: Stocks are increasing. n: Interest rates are steady. r: John will invest in stocks. a). ~n Vr I b). ~(m Vr)arrow_forwardActivity 2: Inductive or Deductive Directions: Read the following statements carefully. Determine if the following argument is best classified as inductive or deductive. Write Inductive if inductive reasoning is used and Deductive for deductive reasoning. Write your answers in your answer sheet. 1. I heard lots of barking last night. The neighbor's dog must've been pretty upset about something, since he rarely barks. 2. All dogs bark. Fido is a dog, so he barks. 3. No book in English begins numbering its pages on a left-hand page. This is a book in English, therefore it will begin its numbering on a right-hand page. 4. On a National Geographic map, no two adjacent nations appear shaded with the same color. Brazil is shaded green on this map, and it is a National Geographic map. Only two nations in South America are not adiacent to Brazil. So, at most three South American nations on this map are shaded green. 5. The overwhelming majority of mutations are not beneficial to an organism's…arrow_forward
- CHECK YOUR PROGRESS 1: Determine whether each of the following arguments is an example of inductive reasoning or deductive reasoning. a. All Gilian Glynn novels are worth reading. The novel Gone Girl is a Gilian Flynn novel. Thus Gone Girl is worth reading. Solution: b. I know I will win a jackpot on this slot machine in the next 10 tries, because it has not paid out any money during the last 45 tries. Solution: ASSESSMENT Use inductive reasoning or deductive reasoning to answer the following questions. Write your answers in the box below. 1. 4,8, 12, 16, 20, 24,? 3. Pick any counting number. Multiply the number by 6. Add 8 to the product. Divide the sum by 2. Subtract 4 from the quotient. The resulting number is twice the original number. 4. Pick any counting number. Multiply by 8. Subtract 4 from the product. Divide the difference by 2. Add 2 to the quotient. The resulting number is four times the original number 5. 2,7,-3,2, -8, –-3,-13, -8,-18,?arrow_forwardLet p and q represent the following statements. p: Interest rates are low. q: It is not time to buy a house. Write the following statement in symbolic form: "Interest rates are not low, and it is not time to buy a house." To enter your response, select the appropriate statement in each of the dropdown boxes, and select the appropriate operation in the middle. If only one statement is used, select "none" for the operation in the middle and the statement in the second dropdown box. Be sure to enter the statements in the same order as in the given sentence. ? VUnone Select an answerarrow_forwardLet p and q represent the following statements. p: Interest rates are low. q: It is not time to buy a house. Write the following statement in symbolic form: "Interest rates are not low, and it is not time to buy a house." To enter your response, select the appropriate statement in each of the dropdown boxes, and select the appropriate operation in the middle. If only one statement is used, select "none" for the operation in the middle and the statement in the second dropdown box. Be sure to enter the statements in the same order as in the given sentence. A OV Onone (Select an answer ?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education
Discrete Mathematics and Its Applications ( 8th I...
Math
ISBN:9781259676512
Author:Kenneth H Rosen
Publisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...
Math
ISBN:9780134392790
Author:Beckmann, Sybilla
Publisher:PEARSON
Thinking Mathematically (7th Edition)
Math
ISBN:9780134683713
Author:Robert F. Blitzer
Publisher:PEARSON
Discrete Mathematics With Applications
Math
ISBN:9781337694193
Author:EPP, Susanna S.
Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)
Math
ISBN:9781259985607
Author:David Sobecki Professor, Brian A. Mercer
Publisher:McGraw-Hill Education
Propositional Logic, Propositional Variables & Compound Propositions; Author: Neso Academy;https://www.youtube.com/watch?v=Ib5njCwNMdk;License: Standard YouTube License, CC-BY
Propositional Logic - Discrete math; Author: Charles Edeki - Math Computer Science Programming;https://www.youtube.com/watch?v=rL_8y2v1Guw;License: Standard YouTube License, CC-BY
DM-12-Propositional Logic-Basics; Author: GATEBOOK VIDEO LECTURES;https://www.youtube.com/watch?v=pzUBrJLIESU;License: Standard Youtube License
Lecture 1 - Propositional Logic; Author: nptelhrd;https://www.youtube.com/watch?v=xlUFkMKSB3Y;License: Standard YouTube License, CC-BY
MFCS unit-1 || Part:1 || JNTU || Well formed formula || propositional calculus || truth tables; Author: Learn with Smily;https://www.youtube.com/watch?v=XV15Q4mCcHc;License: Standard YouTube License, CC-BY