Explanation Consider the argument “If Rita studies, she gets good grades. Rita gets bad grades. Therefore, Rita does not study”. To reduce the argument to one of the known valid or invalid, Let s denote the statement “Rita studies” and g denote the statement “Rita gets good grades”. Therefore, the hypotheses are s → g , ∼ g . Now write the argument step by step as follows: 1. s → g Hypothesis 2

Pearson eText for Finite Mathematics & Its Applications -- Instant Access (Pearson+)

12th Edition

ISBN: 9780137442966

Author: Larry Goldstein, David Schneider

Publisher: PEARSON+

See similar textbooks

Concept explainers

Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities.…

Videos

Question

Chapter 11.5, Problem 12E

To determine

Whether the argument “If Rita studies, she gets good grades. Rita gets bad

grades. Therefore, Rita does not study” is valid or invalid.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.5, Problem 11E

Chapter 11.5, Problem 13E

Students have asked these similar questions

Which conclusion will make a valid argument? "I am going to study for the examination or am going to play mobile legends. I did not play mobile legends." a. Therefore, I studied for the examination. b. Therefore, I played and studied for the examination. C. Therefore, I went to bed. d. Therefore, I did not play mobile legends.

What is the equivalent statement of: "If Abe auditions for the part, he will act in the school play." a. Abe does not audition for the part and he will not act in the school play. b. Abe does not audition for the part. c. Abe does not audition for the part or he would act in the school play. d. If Abe does not audition for the part, he will not act in the school play.

Cooper says, “If Sandy and I are eating dinner together then I order fries or I order dessert.” p->q If Cooper tells you that last night he had fries for dinner, can you logically conclude that he was out with Sandy?

Chapter 11 Solutions

Pearson eText for Finite Mathematics & Its Applications -- Instant Access (Pearson+)

Ch. 11.1 - Determine which of the following sentences are...Ch. 11.1 - Prob. 2CYU Ch. 11.1 - Prob. 1E Ch. 11.1 - In Exercises 1–15, determine which sentences are...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - In Exercises 115, determine which sentences are...Ch. 11.1 - Prob. 8E

Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - In Exercises 115, determine which sentences are...Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - Prob. 15E Ch. 11.1 - In Exercises 16 and 17, give the simple statements...Ch. 11.1 - Prob. 17E Ch. 11.1 - In Exercises 18 and 19, give the simple statements...Ch. 11.1 - In Exercises 18 and 19, give the simple statements...Ch. 11.1 - Prob. 20E Ch. 11.1 - The Smithsonian Museum of Natural History has...Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Let p denote the statement Paris is called the...Ch. 11.1 - Let p denote the statement Ozone is opaque to...Ch. 11.1 - 26. Let p denote the statement “Papyrus is the...Ch. 11.1 - 27. Let a denote the statement “Florida borders...Ch. 11.2 - Construct the truth table for (p~r)q.Ch. 11.2 - Construct the truth table for p~q.Ch. 11.2 - 3. Let p denote “May follows April,” and let q...Ch. 11.2 - In Exercises 14, show that the expressions are...Ch. 11.2 - Prob. 2E Ch. 11.2 - In Exercises 1–4, show that the expressions are...Ch. 11.2 - Prob. 4E Ch. 11.2 - Prob. 5E Ch. 11.2 - Prob. 6E Ch. 11.2 - In Exercises 528, construct truth tables for the...Ch. 11.2 - In Exercises 528, construct truth tables for the...Ch. 11.2 - Prob. 9E Ch. 11.2 - Prob. 10E Ch. 11.2 - Prob. 11E Ch. 11.2 - Prob. 12E Ch. 11.2 - Prob. 13E Ch. 11.2 - Prob. 14E Ch. 11.2 - Prob. 15E Ch. 11.2 - Prob. 16E Ch. 11.2 - Prob. 17E Ch. 11.2 - In Exercises 528, construct truth tables for the...Ch. 11.2 - In Exercises 5–28, construct truth tables for the...Ch. 11.2 - Prob. 20E Ch. 11.2 - Prob. 21E Ch. 11.2 - Prob. 22E Ch. 11.2 - Prob. 23E Ch. 11.2 - Prob. 24E Ch. 11.2 - Prob. 25E Ch. 11.2 - Prob. 26E Ch. 11.2 - Prob. 27E Ch. 11.2 - Prob. 28E Ch. 11.2 - In Exercises 27–30, determine whether statement...Ch. 11.2 - Prob. 30E Ch. 11.2 - Prob. 31E Ch. 11.2 - Prob. 32E Ch. 11.2 - Prob. 33E Ch. 11.2 - Prob. 34E Ch. 11.2 - Let p denote John Lennon was a member of the...Ch. 11.2 - Let m denote the statement The Magna Carta was...Ch. 11.2 - Prob. 37E Ch. 11.2 - Prob. 38E Ch. 11.2 - Prob. 39E Ch. 11.2 - Prob. 40E Ch. 11.2 - Prob. 41E Ch. 11.2 - Prob. 42E Ch. 11.2 - Prob. 43E Ch. 11.2 - Prob. 44E Ch. 11.2 - Prob. 45E Ch. 11.2 - Prob. 46E Ch. 11.2 - Prob. 47E Ch. 11.2 - Prob. 48E Ch. 11.2 - Prob. 49E Ch. 11.2 - Prob. 50E Ch. 11.2 - Prob. 51E Ch. 11.2 - Prob. 52E Ch. 11.3 - 1. Let p denote the statement “A square is a...Ch. 11.3 - Prob. 2CYU Ch. 11.3 - Prob. 1E Ch. 11.3 - Prob. 2E Ch. 11.3 - Prob. 3E Ch. 11.3 - Construct a truth table for each of the statement...Ch. 11.3 - Prob. 5E Ch. 11.3 - Prob. 6E Ch. 11.3 - Prob. 7E Ch. 11.3 - Prob. 8E Ch. 11.3 - Prob. 9E Ch. 11.3 - Prob. 10E Ch. 11.3 - Prob. 11E Ch. 11.3 - Prob. 12E Ch. 11.3 - Prob. 13E Ch. 11.3 - Prob. 14E Ch. 11.3 - Prob. 15E Ch. 11.3 - Prob. 16E Ch. 11.3 - Prob. 17E Ch. 11.3 - Prob. 18E Ch. 11.3 - Prob. 19E Ch. 11.3 - Prob. 20E Ch. 11.3 - Prob. 21E Ch. 11.3 - Prob. 22E Ch. 11.3 - Prob. 23E Ch. 11.3 - Prob. 24E Ch. 11.3 - Prob. 25E Ch. 11.3 - Prob. 26E Ch. 11.3 - In Exercises 2734, write the statement forms in...Ch. 11.3 - Prob. 28E Ch. 11.3 - In Exercises 27–34, write the statement forms in...Ch. 11.3 - Prob. 30E Ch. 11.3 - In Exercises 2734, write the statement forms in...Ch. 11.3 - In Exercises 27–34, write the statement forms in...Ch. 11.3 - Prob. 33E Ch. 11.3 - Prob. 34E Ch. 11.3 - Prob. 35E Ch. 11.3 - Prob. 36E Ch. 11.3 - Prob. 37E Ch. 11.3 - Prob. 38E Ch. 11.3 - Prob. 39E Ch. 11.3 - Prob. 40E Ch. 11.3 - Prob. 41E Ch. 11.3 - Prob. 42E Ch. 11.3 - Prob. 43E Ch. 11.3 - Prob. 44E Ch. 11.3 - Prob. 45E Ch. 11.3 - Prob. 46E Ch. 11.3 - Prob. 47E Ch. 11.3 - Prob. 48E Ch. 11.4 - Prob. 1CYU Ch. 11.4 - Prob. 2CYU Ch. 11.4 - Prob. 3CYU Ch. 11.4 - Prob. 1E Ch. 11.4 - 2. Show that the distributive laws hold:...Ch. 11.4 - Prob. 3E Ch. 11.4 - 4. Without using truth tables, show that . Ch. 11.4 - Prob. 5E Ch. 11.4 - Prob. 6E Ch. 11.4 - Prob. 7E Ch. 11.4 - Prob. 8E Ch. 11.4 - Prob. 9E Ch. 11.4 - Prob. 10E Ch. 11.4 - Prob. 11E Ch. 11.4 - Prob. 12E Ch. 11.4 - Prob. 13E Ch. 11.4 - Prob. 14E Ch. 11.4 - Prob. 15E Ch. 11.4 - Prob. 16E Ch. 11.4 - Prob. 17E Ch. 11.4 - Prob. 18E Ch. 11.4 - Prob. 19E Ch. 11.4 - Prob. 20E Ch. 11.4 - Prob. 21E Ch. 11.4 - Prob. 22E Ch. 11.4 - Prob. 23E Ch. 11.4 - 24. Negate the following statements: (a) Isaac...Ch. 11.4 - Prob. 25E Ch. 11.4 - Prob. 26E Ch. 11.4 - Prob. 27E Ch. 11.4 - Prob. 28E Ch. 11.4 - Prob. 29E Ch. 11.4 - Prob. 30E Ch. 11.4 - Tax Instruction The following statements can be...Ch. 11.4 - Prob. 32E Ch. 11.4 - Prob. 33E Ch. 11.4 - Prob. 34E Ch. 11.5 - Show that the argument is valid. If goldenrod is...Ch. 11.5 - Show by indirect proof that the argument is valid....Ch. 11.5 - Prob. 1E Ch. 11.5 - In Exercises 110, show that the argument is valid....Ch. 11.5 - In Exercises 110, show that the argument is valid....Ch. 11.5 - In Exercises 1–10, show that the argument is...Ch. 11.5 - Prob. 5E Ch. 11.5 - In Exercises 110, show that the argument is valid....Ch. 11.5 - Prob. 7E Ch. 11.5 - Prob. 8E Ch. 11.5 - Prob. 9E Ch. 11.5 - Prob. 10E Ch. 11.5 - Prob. 11E Ch. 11.5 - Prob. 12E Ch. 11.5 - Prob. 13E Ch. 11.5 - Prob. 14E Ch. 11.5 - In Exercises 11–20, test the validity of the...Ch. 11.5 - In Exercises 1120, test the validity of the...Ch. 11.5 - In Exercises 11–20, test the validity of the...Ch. 11.5 - Prob. 18E Ch. 11.5 - Prob. 19E Ch. 11.5 - Prob. 20E Ch. 11.5 - Prob. 21E Ch. 11.5 - Prob. 22E Ch. 11.5 - In Exercises 2124, use indirect proof to show that...Ch. 11.5 - Prob. 24E Ch. 11.5 - Prob. 25E Ch. 11.5 - Prob. 26E Ch. 11.5 - Prob. 27E Ch. 11.5 - Show that each of the arguments in Exercises 27...Ch. 11.6 - Prob. 1CYU Ch. 11.6 - Prob. 2CYU Ch. 11.6 - Prob. 3CYU Ch. 11.6 - Prob. 1E Ch. 11.6 - Prob. 2E Ch. 11.6 - 3. An alert California teacher chided “Dear Abby”...Ch. 11.6 - Prob. 4E Ch. 11.6 - 5. Let the universe be all university professors....Ch. 11.6 - Prob. 6E Ch. 11.6 - Prob. 7E Ch. 11.6 - Prob. 8E Ch. 11.6 - Let the universe consist of all nonnegative...Ch. 11.6 - Let the universe consist of all real numbers. Let...Ch. 11.6 - 11. Negate each statement by changing existential...Ch. 11.6 - Prob. 12E Ch. 11.6 - Prob. 13E Ch. 11.6 - Consider the universe of all subsets of the set...Ch. 11.6 - Prob. 15E Ch. 11.6 - Prob. 16E Ch. 11.6 - Let the universal set be...Ch. 11.6 - Prob. 18E Ch. 11.6 - Prob. 19E Ch. 11.6 - Prob. 20E Ch. 11.7 - (a) Simplify the circuit shown in Fig. 9 by using...Ch. 11.7 - Prob. 1E Ch. 11.7 - 2. Write the logic statement represented by Fig....Ch. 11.7 - Prob. 3E Ch. 11.7 - Prob. 4E Ch. 11.7 - Prob. 5E Ch. 11.7 - Draw the logic circuit that represents each of the...Ch. 11.7 - Prob. 7E Ch. 11.7 - Prob. 8E Ch. 11.7 - Prob. 9E Ch. 11.7 - Prob. 10E Ch. 11.7 - Prob. 11E Ch. 11.7 - Prob. 12E Ch. 11.7 - Prob. 13E Ch. 11.7 - Prob. 14E Ch. 11.7 - Prob. 15E Ch. 11.7 - Prob. 16E Ch. 11.7 - 17. Design a logic circuit that acts as an xor...Ch. 11.7 - Prob. 18E Ch. 11.7 - Prob. 19E Ch. 11.7 - Switch Design for a Lecture Hall In designing a...Ch. 11.7 - Prob. 21E Ch. 11.7 - Use the Wolfram |Alpha function Boolean Minimize...Ch. 11 - 1. What is a logical statement? Ch. 11 - Prob. 2FCCE Ch. 11 - Prob. 3FCCE Ch. 11 - What do we mean by logical equivalence? Explain...Ch. 11 - Prob. 5FCCE Ch. 11 - Prob. 6FCCE Ch. 11 - Prob. 7FCCE Ch. 11 - Prob. 8FCCE Ch. 11 - Prob. 9FCCE Ch. 11 - Prob. 10FCCE Ch. 11 - Prob. 11FCCE Ch. 11 - State De Morgans laws for quantified statements.Ch. 11 - Prob. 1RE Ch. 11 - Prob. 2RE Ch. 11 - Prob. 3RE Ch. 11 - Prob. 4RE Ch. 11 - Prob. 5RE Ch. 11 - Prob. 6RE Ch. 11 - Prob. 7RE Ch. 11 - Prob. 8RE Ch. 11 - Prob. 9RE Ch. 11 - Prob. 10RE Ch. 11 - Prob. 11RE Ch. 11 - Prob. 12RE Ch. 11 - Prob. 13RE Ch. 11 - Prob. 14RE Ch. 11 - Prob. 15RE Ch. 11 - Prob. 16RE Ch. 11 - Prob. 17RE Ch. 11 - 18. Show that the argument is valid: If I shop for...Ch. 11 - Prob. 19RE Ch. 11 - Prob. 20RE Ch. 11 - 21. Draw the logic circuit corresponding to the...Ch. 11 - Prob. 22RE Ch. 11 - Prob. 23RE Ch. 11 - Prob. 24RE Ch. 11 - 25. Construct a statement equivalent to p XOR q,...Ch. 11 - Denise, Miriam, Sally, Nelson, and Bob are...

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.

Whether the argument “If Rita studies, she gets good grades. Rita gets bad grades. Therefore, Rita does not study” is valid or invalid.

Solution Summary: The author explains how to determine whether the argument "If Rita studies, she gets good grades.