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What is the rule of inference used in the following: If I work all night on this homework, then I can answer all the exercises. If I answer all the exercises, I will understand the material. Therefore, if I work all night on this homework, then I will understand the material.

What is the rule of inference used in the following: If I work all night on this homework, then I can answer all the exercises. If I answer all the exercises, I will understand the material. Therefore, if I work all night on this homework, then I will understand the material.

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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**Problem 10 (Rules of Inference)** What is the rule of inference used in the following: If I work all night on this homework, then I can answer all the exercises. If I answer all the exercises, I will understand the material. Therefore, if I work all night on this homework, then I will understand the material. This example illustrates the use of the rule of inference known as *hypothetical syllogism*. In logical terms, hypothetical syllogism is a valid argument form which states: If \( p \rightarrow q \) and \( q \rightarrow r \), then \( p \rightarrow r \). In this problem: - \( p \) represents "I work all night on this homework." - \( q \) represents "I can answer all the exercises." - \( r \) represents "I will understand the material." Using hypothetical syllogism, we conclude that if the first condition is met, the final outcome will also be achieved.
Transcribed Image Text:**Problem 10 (Rules of Inference)** What is the rule of inference used in the following: If I work all night on this homework, then I can answer all the exercises. If I answer all the exercises, I will understand the material. Therefore, if I work all night on this homework, then I will understand the material. This example illustrates the use of the rule of inference known as *hypothetical syllogism*. In logical terms, hypothetical syllogism is a valid argument form which states: If \( p \rightarrow q \) and \( q \rightarrow r \), then \( p \rightarrow r \). In this problem: - \( p \) represents "I work all night on this homework." - \( q \) represents "I can answer all the exercises." - \( r \) represents "I will understand the material." Using hypothetical syllogism, we conclude that if the first condition is met, the final outcome will also be achieved.
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