Let p, q, and r represent the following statements: p: Sam had pizza last night. q: Chris finished her homework. r. Pat watched the news this morning. Give a formula (using appropriate symbols) for the following statements: Sam had pizza last night or Chris didn' finish her homework. O png O *pvq OPV -9
Let p, q, and r represent the following statements: p: Sam had pizza last night. q: Chris finished her homework. r. Pat watched the news this morning. Give a formula (using appropriate symbols) for the following statements: Sam had pizza last night or Chris didn' finish her homework. O png O *pvq OPV -9
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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Can someone help with this please?
![**Logic Statements Exercise**
**Objective:**
Learn how to translate English statements into logical formulas using appropriate symbols.
**Problem Statement:**
Let \( p \), \( q \), and \( r \) represent the following statements:
- \( p \): Sam had pizza last night.
- \( q \): Chris finished her homework.
- \( r \): Pat watched the news this morning.
**Task:**
Give a formula (using appropriate symbols) for the following statement:
"Sam had pizza last night or Chris didn’t finish her homework."
**Options:**
```
O ~ p ∧ q
O ~ p ∨ q
O p ∧ ~ q
O p ∨ ~ q
O r
```
**Explanation:**
The goal is to correctly represent the English statement "Sam had pizza last night or Chris didn’t finish her homework" using the given logical symbols:
- \( p \): Sam had pizza last night.
- \( q \): Chris finished her homework.
- \( \sim q \): Chris didn’t finish her homework (negation of \( q \)).
The given statement utilizes the logical OR operation (represented by \( \vee \)).
Thus, the correct logical formula is:
\[ p \vee \sim q \]
Hence, the correct option to select from the choices given is:
```
O p ∨ ~ q
```
**Note:**
The other options (\(\sim p \land q\), \(\sim p \lor q\), \(p \land \sim q\), and \(r\)) do not accurately represent the given English statement.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1215af52-4a4e-475d-b5dd-45ff7e3fdd22%2Fdcaaac98-3536-400b-b1c2-82b2f9fc7932%2Fkx5i96k_processed.png&w=3840&q=75)
Transcribed Image Text:**Logic Statements Exercise**
**Objective:**
Learn how to translate English statements into logical formulas using appropriate symbols.
**Problem Statement:**
Let \( p \), \( q \), and \( r \) represent the following statements:
- \( p \): Sam had pizza last night.
- \( q \): Chris finished her homework.
- \( r \): Pat watched the news this morning.
**Task:**
Give a formula (using appropriate symbols) for the following statement:
"Sam had pizza last night or Chris didn’t finish her homework."
**Options:**
```
O ~ p ∧ q
O ~ p ∨ q
O p ∧ ~ q
O p ∨ ~ q
O r
```
**Explanation:**
The goal is to correctly represent the English statement "Sam had pizza last night or Chris didn’t finish her homework" using the given logical symbols:
- \( p \): Sam had pizza last night.
- \( q \): Chris finished her homework.
- \( \sim q \): Chris didn’t finish her homework (negation of \( q \)).
The given statement utilizes the logical OR operation (represented by \( \vee \)).
Thus, the correct logical formula is:
\[ p \vee \sim q \]
Hence, the correct option to select from the choices given is:
```
O p ∨ ~ q
```
**Note:**
The other options (\(\sim p \land q\), \(\sim p \lor q\), \(p \land \sim q\), and \(r\)) do not accurately represent the given English statement.
![**Truth Table for Logical Statement**
---
**Task Description:**
Consider the truth table for the following statement:
\[
(p \lor q) \land r
\]
while assuming that the table begins with the following three columns:
\[
\begin{array}{|c|c|c|}
\hline
p & q & r \\
\hline
T & T & T \\
T & T & F \\
T & F & T \\
T & F & F \\
F & T & T \\
F & T & F \\
F & F & T \\
F & F & F \\
\hline
\end{array}
\]
---
**Instructions:**
Select the correct choice for the full statement,
\[
(p \lor q) \land r
\]
- ( )
\[
\begin{array}{|c|c|c|c|}
\hline
p & q & r & (p \lor q) \land r \\
\hline
T & T & T & T \\
T & T & F & F \\
T & F & T & T \\
T & F & F & F \\
F & T & T & T \\
F & T & F & F \\
F & F & T & F \\
F & F & F & F \\
\hline
\end{array}
\]
- ( )
\[
\begin{array}{|c|c|c|c|}
\hline
p & q & r & (p \lor q) \land r \\
\hline
T & T & T & T \\
T & T & F & T \\
T & F & T & T \\
T & F & F & T \\
F & T & T & T \\
F & T & F & T \\
F & F & T & F \\
F & F & F & T \\
\hline
\end{array}
\]
- ( )
\[
\begin{array}{|c|c|c|c|}
\hline
p &](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1215af52-4a4e-475d-b5dd-45ff7e3fdd22%2Fdcaaac98-3536-400b-b1c2-82b2f9fc7932%2F2erm78_processed.png&w=3840&q=75)
Transcribed Image Text:**Truth Table for Logical Statement**
---
**Task Description:**
Consider the truth table for the following statement:
\[
(p \lor q) \land r
\]
while assuming that the table begins with the following three columns:
\[
\begin{array}{|c|c|c|}
\hline
p & q & r \\
\hline
T & T & T \\
T & T & F \\
T & F & T \\
T & F & F \\
F & T & T \\
F & T & F \\
F & F & T \\
F & F & F \\
\hline
\end{array}
\]
---
**Instructions:**
Select the correct choice for the full statement,
\[
(p \lor q) \land r
\]
- ( )
\[
\begin{array}{|c|c|c|c|}
\hline
p & q & r & (p \lor q) \land r \\
\hline
T & T & T & T \\
T & T & F & F \\
T & F & T & T \\
T & F & F & F \\
F & T & T & T \\
F & T & F & F \\
F & F & T & F \\
F & F & F & F \\
\hline
\end{array}
\]
- ( )
\[
\begin{array}{|c|c|c|c|}
\hline
p & q & r & (p \lor q) \land r \\
\hline
T & T & T & T \\
T & T & F & T \\
T & F & T & T \\
T & F & F & T \\
F & T & T & T \\
F & T & F & T \\
F & F & T & F \\
F & F & F & T \\
\hline
\end{array}
\]
- ( )
\[
\begin{array}{|c|c|c|c|}
\hline
p &
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