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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 3.5, Problem 49ES

Textbook Problem

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Use all of the premises to determine a valid conclusion for the given argument.

If it is a theropod, then it is not herbivorous. If it is not herbivorous, then it is not a sauropod, It is a sauropod. Therefore, _____________

To determine

**To identify::**

A valid conclusion for the given argument using all the premises.

**Given information::**

The argument "If it is a theropod, then it is not herbivorous. If it is not herbivorous, then it is not a sauropod. It is sauropod. Therefore, _____________"

**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.

__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 | |

| | | | |

Table 3.16 shows to two symbolic forms associated with invalid arguments. Any argument that has one of these symbolic forms is invalid.

Table 3.16 Standard Forms of TWO Invalid Arguments | |

Fallacy of the converse | Fallacy of the inverse |

| |

Logical Equivalences involving Conditional Statements | |

**Calculation:**

The argument "If it is a theropod, then it is not herbivorous. If it is not herbivorous, then it is not a sauropod. It is sauropod. Therefore, _____________" in symbolic form is given by: | |

Identifying the Premises 1, Premises 2, Premises 3 and Conclusion of the given argument as follows: | |

Mathematical Excursions (MindTap Course List)

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Every...Ch. 3 - Write each statement in If p, then q form. Being...Ch. 3 - Write each statement in If p, then q form. I could...Ch. 3 - Write each statement in If p, then q form. Being...Ch. 3 - Write the a. converse, b. inverse, and c....Ch. 3 - Write the a. converse, b. inverse, and c....Ch. 3 - Write the a. converse, b. inverse, and c....Ch. 3 - Write the a. converse, b. inverse, and c....Ch. 3 - Write the a. converse, b. inverse, and c....Ch. 3 - Write the a. converse, b. inverse, and c....Ch. 3 - What is the inverse of the contrapositive of pq?Ch. 3 - Use the contrapositive of the following statement...Ch. 3 - Determine the original statement if the given...Ch. 3 - Determine the original statement if the given...Ch. 3 - Determine the original statement if the given...Ch. 3 - Determine the original statement if the given...Ch. 3 - Use a truth table to determine whether the...Ch. 3 - Use a truth table to determine whether the...Ch. 3 - Use a truth table to determine whether the...Ch. 3 - Use a truth table to determine whether the...Ch. 3 - Determine whether the argument is valid or invalid...Ch. 3 - Determine whether the argument is valid or invalid...Ch. 3 - Determine whether the argument is valid or invalid...Ch. 3 - Determine whether the argument is valid or invalid...Ch. 3 - Determine whether the argument is valid or invalid...Ch. 3 - Determine whether the argument is valid or invalid...Ch. 3 - Use an Euler diagram to determine whether the...Ch. 3 - Use an Euler diagram to determine whether the...Ch. 3 - Use an Euler diagram to determine whether the...Ch. 3 - Use an Euler diagram to determine whether the...Ch. 3 - Determine whether each sentence is a statement. a....Ch. 3 - Write the negation of each statement. 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