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(7) Determine whether the following argument form is valid or invalid by using a truth table. 1. ~Q~P 2. PA~Q RV P

(7) Determine whether the following argument form is valid or invalid by using a truth table. 1. ~Q~P 2. PA~Q RV P

Advanced Engineering Mathematics
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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**Determine whether the following argument form is valid or invalid by using a truth table.** 1. \( \sim Q \rightarrow \sim P \) 2. \( P \land \sim Q \) ∴ \( R \lor \sim P \) **Explanation:** This is a logical argument that consists of premises 1 and 2, and a conclusion. The goal is to determine if the argument is valid—that is, if the premises logically lead to the conclusion. To analyze this, a truth table can be used. A truth table will list all possible truth values (True or False) for each variable (P, Q, and R) and show whether the premises and conclusion hold under those conditions. For each combination of truth values: - Evaluate \( \sim Q \rightarrow \sim P \) - Determine \( P \land \sim Q \) - Finally, verify if \( R \lor \sim P \) follows from these conditions. This systematic approach helps in determining the validity of the logical argument. If the premises hold true but the conclusion does not in any scenario, the argument is considered invalid.
Transcribed Image Text:**Determine whether the following argument form is valid or invalid by using a truth table.** 1. \( \sim Q \rightarrow \sim P \) 2. \( P \land \sim Q \) ∴ \( R \lor \sim P \) **Explanation:** This is a logical argument that consists of premises 1 and 2, and a conclusion. The goal is to determine if the argument is valid—that is, if the premises logically lead to the conclusion. To analyze this, a truth table can be used. A truth table will list all possible truth values (True or False) for each variable (P, Q, and R) and show whether the premises and conclusion hold under those conditions. For each combination of truth values: - Evaluate \( \sim Q \rightarrow \sim P \) - Determine \( P \land \sim Q \) - Finally, verify if \( R \lor \sim P \) follows from these conditions. This systematic approach helps in determining the validity of the logical argument. If the premises hold true but the conclusion does not in any scenario, the argument is considered invalid.
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