Using the assigned letters, write the compound statement given below in symbols. r= "The food is good." p = "I eat too much." q = "'ll exercise." The food is good and if I eat too much, then l'll exercise. O (r^ p) ->q O (r-> p)vq Or^ (p -> q) O (rv p) -> q
Using the assigned letters, write the compound statement given below in symbols. r= "The food is good." p = "I eat too much." q = "'ll exercise." The food is good and if I eat too much, then l'll exercise. O (r^ p) ->q O (r-> p)vq Or^ (p -> q) O (rv p) -> q
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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Transcribed Image Text:**Using the assigned letters, write the compound statement given below in symbols.**
**r** = "The food is good."
**p** = "I eat too much."
**q** = "I'll exercise."
_The food is good and if I eat too much, then I'll exercise._
- ⭕ (r ∧ p) -> q
- ⭕ (r -> p) ∨ q
- ⭕ r ∧ (p -> q)
- ⭕ (r ∨ p) -> q
![**Determine the truth value of the statement:**
\[ (-4 \in \mathbb{N}) \vee (3 \in 2\mathbb{Z}) \]
**Options:**
- O True
- O False
- O It cannot be determined whether it is true or false.
---
**Explanation:**
This problem involves evaluating a logical statement composed of two parts with set membership and using the logical OR operator.
1. \( -4 \in \mathbb{N} \)
- \(\mathbb{N}\) denotes the set of natural numbers (typically starting from 1). Since \(-4\) is not a natural number, this statement is false.
2. \( 3 \in 2\mathbb{Z} \)
- \(2\mathbb{Z}\) denotes the set of even integers. Since \(3\) is not an even integer, this statement is also false.
For the entire expression \((\text{False}) \vee (\text{False})\), the logical OR operator (\(\vee\)) results in false if both operands are false. Hence, the overall statement is false.
So, the correct answer is:
- O **False**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1215af52-4a4e-475d-b5dd-45ff7e3fdd22%2Ff56bb5d8-ff71-40ce-a501-6e8c240283e6%2F9qxaeng_processed.png&w=3840&q=75)
Transcribed Image Text:**Determine the truth value of the statement:**
\[ (-4 \in \mathbb{N}) \vee (3 \in 2\mathbb{Z}) \]
**Options:**
- O True
- O False
- O It cannot be determined whether it is true or false.
---
**Explanation:**
This problem involves evaluating a logical statement composed of two parts with set membership and using the logical OR operator.
1. \( -4 \in \mathbb{N} \)
- \(\mathbb{N}\) denotes the set of natural numbers (typically starting from 1). Since \(-4\) is not a natural number, this statement is false.
2. \( 3 \in 2\mathbb{Z} \)
- \(2\mathbb{Z}\) denotes the set of even integers. Since \(3\) is not an even integer, this statement is also false.
For the entire expression \((\text{False}) \vee (\text{False})\), the logical OR operator (\(\vee\)) results in false if both operands are false. Hence, the overall statement is false.
So, the correct answer is:
- O **False**
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