Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
3rd Edition
ISBN: 9780134689555
Author: Edgar Goodaire, Michael Parmenter
Publisher: PEARSON
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Chapter 1.2, Problem 10TFQ
Disjunctive normalform is useful in applications of logic to computer science.
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Can you please answer all the following grade 12 advanced functions questions. I will make sure to leave a thumbs up on the answer if it is written by hand on paper without ai. Thanks a lot!
18. Consider the functions f(x) = and g(x) = 3*.
x-3
a) Write a simplified equation that represents f-1 (g(x)).*
b) State the domain and range of f-1 (g(x)).
20. After a school dance, Carlos is thinking of asking Keiko out on a date.
The probability that Carlos will ask can be modeled by the function
f(x)=0.45 sin x + 0.5, and the probability that Keiko will say yes
can be modeled by the function g(x) = -0.08x(x-7), where x
represents the number of days following the school dance.
The conditional probability that Carlos asks Keiko and Keiko says yes
can be modeled by the combined function y = f(x)g(x). This
combined function is shown on the graph.
y
15
Answers to the following questions are approximate. Answers may vary but all reasonable answers will be accepted.
a) Use the graph to approximate: How many days after the dance should Carlos ask Keiko to go out with him?
x
b) Use the graph to approximate: If Carlos asks Keiko on the day that you recommended above, approximately what is the
probability that they will go on the date?
c) According to the graph, at what point does Carlos have absolutely no chance of dating Keiko?
Chapter 1 Solutions
Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Ch. 1.1 - True/False Questions
“” means “”
Ch. 1.1 - A truth table based on four simple statements...Ch. 1.1 - True/False Questions
2. If is true, then is also...Ch. 1.1 - If p and q are both false, the truth value of...Ch. 1.1 - If pq is false, the truth value of (pq)(pq) is...Ch. 1.1 - pq andqp are logically equivalent.Ch. 1.1 - True/False Questions
7. A statement and its...Ch. 1.1 - (pq)(pq) is a tautology.Ch. 1.1 - True/False Questions
9. If B is a tautology and A...Ch. 1.1 - True/False Questions
10. If A and B are both...
Ch. 1.1 - Construct a truth table for each of the following...Ch. 1.1 - (a) If pq is false, determine the truth value of...Ch. 1.1 - 3. Determine the truth value for
when are all...Ch. 1.1 - 4. Repeat Exercise 3 in the case where are all...Ch. 1.1 - 5. (a) Show that is a tautology.
(b) Show that ...Ch. 1.1 - Prob. 6ECh. 1.1 - Prob. 7ECh. 1.1 - Prob. 8ECh. 1.1 - Prob. 9ECh. 1.1 - 10. (a) Show that the statement is not logically...Ch. 1.1 - 11. If and are statements, then the compound...Ch. 1.2 - True/False Questions
Two statements A and B are...Ch. 1.2 - True/False Questions
2. “A B” and “A B” mean the...Ch. 1.2 - True/False Questions
3. () () for any statement ....Ch. 1.2 - True/False Questions
4. for any statements
Ch. 1.2 - (p(qr))((pq)(pr)) for any statements p,q,r.Ch. 1.2 - ((pq))((p)(q)) for any statements p,q.Ch. 1.2 - If A Band C is any statement, then (A C) (B ...Ch. 1.2 - True/False Questions
8. is in disjunctive normal...Ch. 1.2 - (pq(r))((p)(q)(r)) is in disjunctive normal form.Ch. 1.2 - True/False Questions
10. Disjunctive normal form...Ch. 1.2 - Prob. 1ECh. 1.2 - (a) Show that p[(pq)] is a tautology. (b) What is...Ch. 1.2 - Simplify each of the following statements. (a)...Ch. 1.2 - 4. Using truth tables, verify the following...Ch. 1.2 - 5. Using the properties in the text together with...Ch. 1.2 - Prove that the statements (p(q))q and (p(q))p are...Ch. 1.2 - Prob. 7ECh. 1.2 - Prob. 8ECh. 1.2 - Prob. 9ECh. 1.2 - Express each of the following statements in...Ch. 1.2 - Find out what you can about Augustus De Morgan and...Ch. 1.3 - True/False Questions
An argument is valid if,...Ch. 1.3 - Prob. 2TFQCh. 1.3 - Prob. 3TFQCh. 1.3 - True/False Questions
4. De Morgan’s laws are two...Ch. 1.3 - The chain rule has pq and qr as its premises.Ch. 1.3 - Prob. 6TFQCh. 1.3 - Prob. 7TFQCh. 1.3 - Prob. 8TFQCh. 1.3 - Prob. 9TFQCh. 1.3 - Prob. 10TFQCh. 1.3 - Determine whether or not each of the following...Ch. 1.3 - 2. Verify that each of the five rules of inference...Ch. 1.3 - Verify that each of the following arguments is...Ch. 1.3 - Test the validity of each of the following...Ch. 1.3 - 5. Determine the validity of each of the following...Ch. 1.3 - Prob. 6ECh. 1.3 - Prob. 7ECh. 1.3 - Prob. 8ECh. 1.3 - Prob. 9ECh. 1.3 - 10. What language is being used when we say “modus...Ch. 1 - Construct a truth table for the compound statement...Ch. 1 - Determine the truth value of [p(q((r)s))](rt),...Ch. 1 - 3. Determine whether each statement is a...Ch. 1 - Two compound statements A and B have the property...Ch. 1 - 5. (a) Suppose A, B, and C are compound statements...Ch. 1 - Establish the logical equivalence of each of the...Ch. 1 - 7. Express each of the following statements in...Ch. 1 - Determine whether each of the following arguments...Ch. 1 - Discuss the validity of the argument pq(p)r Purple...Ch. 1 - 10. Determine the validity of each of the...
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- Can you please answer all the following grade 12 advanced functions questions. I will make sure to leave a thumbs up if it's handwritten and on paper without ai. Thanks!arrow_forward26. The two functions shown represent the height vs. time graphs for two bouncing balls. Height is measured in feet, and time is measured in seconds. a) Determine the approximate time interval when the two balls are less than 2 ft apart. 20 16 12 8 4 0 1 2 b) At what time was the difference in height between the two balls the greatest? 3 4 5 27. A function f(x) has zeros at x = ±7 and x = -2. Another function g(x) has zeros at x = 7 and x = 0. State the zeros of the function y = = g(x) f(x). Explain how you know.arrow_forwardCan you please answer all the following grade 12 advanced functions questions. I will make sure to leave a thumbs up on the answer if it is written by hand on paper without ai. Thanks a lot!arrow_forward
- 16. The table of values shows some key points on the functions f(x) and g(x). Evaluate the following. a) 2 g(f(2)) b) f(g(-1)) χ y = f(x) y = g(x) -1 0 9 0 1 -2 1 2 12 2 -1 -8arrow_forward24. Suppose that f(x) and g(x) are two distinct non-zero functions. State the condition that is needed to satisfy each of the following. a) f(x)g(x) = g(x) b) f(x)g(x) = 1 c) f(g(x)) = 25. If f(x) = log(x-4) and g(x) =, for what value(s) of x is g(f(x)) undefined? Show your thinking. x+4arrow_forwardCan you please answer all the following grade 12 advanced functions questions. I will make sure to leave a thumbs up on the answer if it is written by hand on paper without ai. Thanks a lot!arrow_forward
- 13. If f(x) = ½ and g(x) = x²-x-72, determine the equation(s) of all asymptote(s) of f(g(x)).arrow_forwardCan you please answer all the following grade 12 advanced functions questions. I will make sure to leave a thumbs up on the answer if it is written by hand on paper without ai. Thanks!arrow_forward22. Jack and Jill work at the same store. The total weekly salary of each employee can be represented by the functions shown, where S represents weekly salary, in dollars, and x represents the number of items sold. Assuming that they sell the same number of items in a week, what is the minimum number of items they have to sell so that Jill's weekly salary is at least $100 more than Jack's? JACK: S = 100 + 5x JILL: S=80+6x 23. You are given the following two functions: f(x)=2x-3 9(x) = −2 (¹)²**5 + 18 2x+5 Your teacher claims that the zero of the function g(f(x)) is greater than the zero of g(x). Prove or disprove your teacher's claim. Show all your work.arrow_forward
- Can you please answer all the following grade 12 advanced functions multiple choice questions. I will make sure to leave a thumbs up on the answer if it is written by hand on paper without ai. Thanks!arrow_forward11. Consider the functions f(x) = 16* and g(x) = -sin x. Determine the value of ƒ (g(-2)). 12. Given functions below, determine h(-6). f(x) = -2x g(x)=√=x+x h(x) = g(f(x))arrow_forwardProve: {a,{a,b}}={c,{c,d}} ⟺ a=c and b=d.arrow_forward
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