Explanation Given information: If we serve lasagna, then Eva will not come to our dinner party. We did not serve lasagna. Therefore, Eva came to our dinner party. Concept Involved: An Argument and a Valid Argument : An argument consists of a set of statements called premises and another statement called the conclusion. An argument is valid if the conclusion is true whenever all the premises are assumed to be true. An argument is invalid if it is not a valid argument. A symbolic argument consists of a set of premises and a conclusion. It is called a symbolic argument because we generally write it in symbolic form to determine its validity. A disjunction is a compound statement formed by joining two statements with the connector OR. The disjunction "p or q" is symbolized by p ∨ q . A disjunction is false if and only if both statements are false; otherwise it is true. A conjunction is a compound statement formed by joining two statements with the connector AND. The conjunction "p and q" is symbolized by p ∧ q . A conjunction is true when both of its combined parts are true; otherwise it is false. A conditional statement, symbolized by p → q , is an if-then statement in which p is a hypothesis and q is a conclusion. The logical connector in a conditional statement is denoted by the symbol → . The conditional is defined to be true unless a true hypothesis leads to a false conclusion. A biconditional statement is defined to be true whenever both parts have the same truth value. The biconditional operator is denoted by a double-headed arrow ↔ . The biconditional p ↔ q represents "p if an only if q", where p is a hypothesis and q is a conclusion. Standard Forms: Arguments can be show to be valid if they have the same symbolic form as an argument that is known to be valid. Table 3.15 shows four symbolic forms and the name used to identify each form. Any argument that has a symbolic form identical to one of these symbolic forms is a valid argument. Table 3.15 Standard Forms of Four Valid Arguments Direct Reasoning Contrapositive Reasoning Transitive Reasoning Disjunctive Reasoning p → q p _ ∴ q p → q ~ q _ ∴ ~ p p → q q → r _ ∴ p → r p ∨ q ~ p _ ∴ q p ∨ q ~ q _ ∴ p Table 3.16 shows to two symbolic forms associated with invalid arguments. Any argument that has one of these symbolic forms is invalid. Disjunctive Standard Forms of TWO Invalid Arguments Fallacy of the converse Fallacy of the inverse p → q q _ ∴ p p → q ~ p _ ∴ ~ q Calculation: In the argument given, the two premises and the conclusion are shown below

WebAssign Printed Access Card for Aufmann/Lockwood/Nation/Clegg's Mathematical Excursions, 4th Edition, Single-Term

4th Edition

ISBN: 9781337652445

Author: Richard N. Aufmann, Joanne Lockwood, Richard D. Nation, Daniel K. Clegg

Publisher: Cengage Learning

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 3, Problem 88RE

To determine

To identify:

Whether the given argument is valid or invalid by comparing its symbolic form with the standard forms given in Tables 3.15 and 3.16 and for each valid argument, state the name of its standard form.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3, Problem 87RE

Chapter 3, Problem 89RE

Students have asked these similar questions

read chapter 10 welding principles and applications, short-circuiting, transfer, GMAW – S. Explain why the power supply is critical in the short-circuiting transfer process. Discuss what happens if there’s too much or two little inductance.

Find the equation of the line / in the figure below. Give exact values using the form y = mx + b. m = b = y WebAssign Plot f(x) = 10* log 9 X

a. Find the general flow pattern of the network shown in the figure. b. Assuming that the flow must be in the directions indicated, find the minimum flows in the branches denoted by X2, X3, X4, and x5 a. Choose the correct answer below and fill in the answer boxes to complete your choice. OA. x₁ = X2 is free X3 is free B. X₁ is free x2= ×4 is free X5 is free X6 = X3= X4 X5 X6 = 11 = ○ C. D. X2 is free X3= X4 is free X5 is free x2 = 0 X3 is free ×4 = X6 is free gave 20 30 12 C 804 60-> B <<90 314 X4D -80 E T 20 40 x

Chapter 3 Solutions

WebAssign Printed Access Card for Aufmann/Lockwood/Nation/Clegg's Mathematical Excursions, 4th Edition, Single-Term

Ch. 3.1 - Write a symbolic statement to represent each of...Ch. 3.1 - Write a symbolic statement to represent each of...Ch. 3.1 - Write a symbolic statement to represent each of...Ch. 3.1 - Write a symbolic statement to represent each of...Ch. 3.1 - Write a symbolic statement to represent each of...Ch. 3.1 - Write a symbolic statement to represent each of...Ch. 3.1 - Which of the networks in Excursion Exercises 1 to...Ch. 3.1 - Which of the networks in Excursion Exercises I to...Ch. 3.1 - Draw a network to represent each statement....Ch. 3.1 - Draw a network to represent each statement. P[...

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 given argument is valid or invalid by comparing its symbolic form with the standard forms given in Tables 3.15 and 3.16 and for each valid argument, state the name of its standard form.

Solution Summary: The author explains the difference between a valid and invalid argument by comparing its symbolic form with the standard forms given in Tables 3.15 and 3.16.

Concept explainers

Videos

To identify: Whether the given argument is valid or invalid by comparing its symbolic form with the standard forms given in Tables 3.15 and 3.16 and for each valid argument, state the name of its standard form.

Want to see the full answer?

Chapter 3 Solutions

To identify:

Whether the given argument is valid or invalid by comparing its symbolic form with the standard forms given in Tables 3.15 and 3.16 and for each valid argument, state the name of its standard form.