Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question

GIVE A TRUTH TABLE

### Logical Implications and Biconditionals **Expression**: \((b) \quad (p \rightarrow q) \rightarrow (q \rightarrow p)\) #### Explanation: In logic, the expression \((p \rightarrow q) \rightarrow (q \rightarrow p)\) describes a scenario where the implication from \(p\) to \(q\) leads to the reverse implication from \(q\) to \(p\). Here's a breakdown: - **\(p \rightarrow q\)**: This implies that if \(p\) is true, then \(q\) must also be true. - **\(q \rightarrow p\)**: Conversely, this states that if \(q\) is true, then \(p\) must also be true. - **Overall Expression**: The expression as a whole \((p \rightarrow q) \rightarrow (q \rightarrow p)\) suggests that if the first implication \((p \rightarrow q)\) holds true, then the implication \((q \rightarrow p)\) should also hold true. Understanding such logical implications is fundamental in fields such as mathematics, computer science, and philosophy, where logical reasoning is crucial.
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Transcribed Image Text:### Logical Implications and Biconditionals **Expression**: \((b) \quad (p \rightarrow q) \rightarrow (q \rightarrow p)\) #### Explanation: In logic, the expression \((p \rightarrow q) \rightarrow (q \rightarrow p)\) describes a scenario where the implication from \(p\) to \(q\) leads to the reverse implication from \(q\) to \(p\). Here's a breakdown: - **\(p \rightarrow q\)**: This implies that if \(p\) is true, then \(q\) must also be true. - **\(q \rightarrow p\)**: Conversely, this states that if \(q\) is true, then \(p\) must also be true. - **Overall Expression**: The expression as a whole \((p \rightarrow q) \rightarrow (q \rightarrow p)\) suggests that if the first implication \((p \rightarrow q)\) holds true, then the implication \((q \rightarrow p)\) should also hold true. Understanding such logical implications is fundamental in fields such as mathematics, computer science, and philosophy, where logical reasoning is crucial.
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