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Construct a truth table for the statement r-(pvq). P T T F q OTTE TFT r pvq r→(pvq) T F T F F F F F + LLU T T T F F T F F (...)

Construct a truth table for the statement r-(pvq). P T T F q OTTE TFT r pvq r→(pvq) T F T F F F F F + LLU T T T F F T F F (...)

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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**Constructing a Truth Table for the Statement \( r \rightarrow (p \lor q) \):** This table displays the logical evaluation of the compound statement \( r \rightarrow (p \lor q) \). It is structured to show all possible truth values for the statements \( p \), \( q \), and \( r \), as well as the intermediate and final evaluations of the logical connectives. | \( p \) | \( q \) | \( r \) | \( p \lor q \) | \( r \rightarrow (p \lor q) \) | |---------|---------|---------|----------------|-----------------------------| | T | T | T | T | | | T | T | F | T | | | T | F | T | T | | | T | F | F | T | | | F | T | T | T | | | F | T | F | T | | | F | F | T | F | | | F | F | F | F | | **Explanation of Columns:** - **\( p \)**, **\( q \)**, and **\( r \)**: These columns represent all possible truth values (True or False) for the given propositions. - **\( p \lor q \)**: This column shows the result of the logical "or" operation between \( p \) and \( q \). The result is True if at least one of the propositions \( p \) or \( q \) is True. - **\( r \rightarrow (p \lor q) \)**: This column reflects the result of the implication \( r \rightarrow (p \lor q) \). The implication is True unless \( r \) is True and \( (p \lor q) \) is False. **Instructions for Completion:** Fill in the truth values for each row based on the logical operations in the \( p \lor q \) and \( r \rightarrow (p \lor q) \) columns.
Transcribed Image Text:**Constructing a Truth Table for the Statement \( r \rightarrow (p \lor q) \):** This table displays the logical evaluation of the compound statement \( r \rightarrow (p \lor q) \). It is structured to show all possible truth values for the statements \( p \), \( q \), and \( r \), as well as the intermediate and final evaluations of the logical connectives. | \( p \) | \( q \) | \( r \) | \( p \lor q \) | \( r \rightarrow (p \lor q) \) | |---------|---------|---------|----------------|-----------------------------| | T | T | T | T | | | T | T | F | T | | | T | F | T | T | | | T | F | F | T | | | F | T | T | T | | | F | T | F | T | | | F | F | T | F | | | F | F | F | F | | **Explanation of Columns:** - **\( p \)**, **\( q \)**, and **\( r \)**: These columns represent all possible truth values (True or False) for the given propositions. - **\( p \lor q \)**: This column shows the result of the logical "or" operation between \( p \) and \( q \). The result is True if at least one of the propositions \( p \) or \( q \) is True. - **\( r \rightarrow (p \lor q) \)**: This column reflects the result of the implication \( r \rightarrow (p \lor q) \). The implication is True unless \( r \) is True and \( (p \lor q) \) is False. **Instructions for Completion:** Fill in the truth values for each row based on the logical operations in the \( p \lor q \) and \( r \rightarrow (p \lor q) \) columns.
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