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a)find a proposition using only p, q, and ~ (negation) and V (or)  b) find a propostion with three variables p, q, and r that is false when at least one of the prepositons is true and is true otherwise

a)find a proposition using only p, q, and ~ (negation) and V (or)  b) find a propostion with three variables p, q, and r that is false when at least one of the prepositons is true and is true otherwise

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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a)find a proposition using only p, q, and ~ (negation) and V (or) 

b) find a propostion with three variables p, q, and r that is false when at least one of the prepositons is true and is true otherwise 

The table represents a logical function with inputs \( p \) and \( q \) and an unidentified output. It appears to be organized into four rows, each representing different combinations of the input values: - When \( p = 1 \) and \( q = 1 \), the output is 1. - When \( p = 1 \) and \( q = 0 \), the output is 1. - When \( p = 0 \) and \( q = 1 \), the output is 0. - When \( p = 0 \) and \( q = 0 \), the output is 1. This truth table suggests that the unidentified function could be a combination of logical operations, such as a NOR or another similar operation.
Transcribed Image Text:The table represents a logical function with inputs \( p \) and \( q \) and an unidentified output. It appears to be organized into four rows, each representing different combinations of the input values: - When \( p = 1 \) and \( q = 1 \), the output is 1. - When \( p = 1 \) and \( q = 0 \), the output is 1. - When \( p = 0 \) and \( q = 1 \), the output is 0. - When \( p = 0 \) and \( q = 0 \), the output is 1. This truth table suggests that the unidentified function could be a combination of logical operations, such as a NOR or another similar operation.
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