Finite Mathematics for the Managerial, Life, and Social Sciences
12th Edition
ISBN: 9781337405782
Author: Soo T. Tan
Publisher: Cengage Learning
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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.
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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.
1. Determine which of the following are statements, and classify each statement as either true or false.
(a) President George Washington was born in (e) Close the door.
Alabama.
(1) 2.3=7.
(g) 3x = 6.
(h) Help stop inflation.
(b) Good morning.
(c) 5+4=9.
(d) x+5=8.
2. Ifp is T and q is F, find the truth values of these statements. The form~() represents the negation of
everything inside the parentheses.
(a) (~p) ^q
(b) (~p) v (~q)
(c) ~(pvq)
3.
Find the truth values of the statements in Exercise 2 if p is T and q is T.
4. Find the truth values of the statements in Exercise 2 if p is F and q is F.
5.
In each of the parts that follow, construct two statements-one using and and the other using or-and
find the truth values of each.
(d) ~ (p ^ q)
(e) ~[(~p) ^q]
(f) ~(pv~q)
(a) November has 30 days. Thanksgiving is always on November 25.
(b) The smallest counting number is 2. 10 is not a multiple of 5.
(c) 2+3=4+1.
8.6 4.12.
(d) Triangles are not squares. 3 is smaller than 5.
6. Translate…
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
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- 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_forwardDetermine if the statements below are True or False. If it’s True, explain why. If it’s False,explain why not, or simply give an example demonstrating why it’s false. A correct choiceof ”True” or ”False” with no explanation will not receive any credit.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
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