### Determining the Validity of Arguments**Exercise:**Determine the validity of each of the following arguments. If the argument is one of those listed in the text, name it.1. She uses e-commerce or she pays by credit card.2. She does not pay by credit card.3. ____________________________4. She uses e-commerce.This exercise asks you to assess if the given arguments lead to a valid conclusion. **Given Argument Breakdown:**- **Premise 1:** She uses e-commerce or she pays by credit card.- **Premise 2:** She does not pay by credit card.- **Conclusion:** She uses e-commerce.### Explanation of the ArgumentIn logical terms, this argument employs the concept of disjunction (logical "or") and negation to arrive at a conclusion.- **Symbolic Form:** - P1: \( P \lor Q \) (She uses e-commerce or she pays by credit card.) - P2: \( \neg Q \) (She does not pay by credit card.) - Conclusion: \( P \) (She uses e-commerce.)According to the rules of logical reasoning, specifically Disjunctive Syllogism, if a disjunction (\( P \lor Q \)) is true and one of the components (Q) is false (\( \neg Q \)), then the other component (P) must be true.### ConclusionFrom the given premises, we can validly conclude that she uses e-commerce. This argument is an example of a Disjunctive Syllogism.**Note:** Understanding and identifying the form of logical arguments is a critical skill in logical reasoning and helps in constructing valid conclusions from given premises. **Title: Verification of Logical Argument Validity****Introduction:**In this tutorial, we will verify the validity of a logical argument using propositional logic techniques.**Given Argument:**The argument to verify consists of the following premises and conclusion:1. \( p \rightarrow q \)2. \( q \rightarrow r \)3. Conclusion: \( (p \lor q) \rightarrow r \)**Steps for Verification:**1. **Understand the Premises and Conclusion:** - Premise 1: \( p \rightarrow q \) - This indicates that if proposition \( p \) is true, then proposition \( q \) must also be true. - Premise 2: \( q \rightarrow r \) - This indicates that if proposition \( q \) is true, then proposition \( r \) must also be true. - Conclusion: \( (p \lor q) \rightarrow r \) - This indicates that if either proposition \( p \) or \( q \) (or both) are true, then proposition \( r \) must be true.2. **Construct a Truth Table:** To verify the validity, we construct a truth table considering the truth values for each proposition \( p \), \( q \), and \( r \). | \( p \) | \( q \) | \( r \) | \( p \rightarrow q \) | \( q \rightarrow r \) | \( p \lor q \) | \( (p \lor q) \rightarrow r \) | |--------|--------|--------|----------------------|----------------------|----------------|--------------------------| | T | T | T | T | T | T | T | | T | T | F | T | F | T | F | | T | F | T | F | T | T | T | | T | F | F | F | T | T | F | | F | T | T | T | T | T | T | | F | T

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Determine the validity of each the following arguments. If the argument is one of those listed in the text, name it. She uses e-commerce or she pays by credit card. She does not pay by credit card. She uses e-commerce.

Determine the validity of each the following arguments. If the argument is one of those listed in the text, name it. She uses e-commerce or she pays by credit card. She does not pay by credit card. She uses e-commerce.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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