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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**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
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**
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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