Let: p: It is October. q: Earth revolves around the sun. Is true or false?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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**Logical Proposition Exercise**

Given Identifiers:
- Let:
  - \( p: \) It is October.
  - \( q: \) Earth revolves around the sun.

Logical Expression:
- Evaluate: \( p \land \sim q \)

Question:
- Is this expression true or false?

Options:
- False (selected option)
- True

**Explanation:**

The expression \( p \land \sim q \) involves a logical "and" (\( \land \)) operator and a negation (\( \sim \)) of \( q \).

- \( p \) is the statement "It is October."
- \( q \) is the statement "Earth revolves around the sun."
- \( \sim q \) is the negation: "Earth does not revolve around the sun."

For \( p \land \sim q \) to be true, both \( p \) must be true and \( \sim q \) must be true simultaneously. Since \( q \) ("Earth revolves around the sun") is a true statement, \( \sim q \) becomes false. Therefore, the entire expression \( p \land \sim q \) is false.
Transcribed Image Text:**Logical Proposition Exercise** Given Identifiers: - Let: - \( p: \) It is October. - \( q: \) Earth revolves around the sun. Logical Expression: - Evaluate: \( p \land \sim q \) Question: - Is this expression true or false? Options: - False (selected option) - True **Explanation:** The expression \( p \land \sim q \) involves a logical "and" (\( \land \)) operator and a negation (\( \sim \)) of \( q \). - \( p \) is the statement "It is October." - \( q \) is the statement "Earth revolves around the sun." - \( \sim q \) is the negation: "Earth does not revolve around the sun." For \( p \land \sim q \) to be true, both \( p \) must be true and \( \sim q \) must be true simultaneously. Since \( q \) ("Earth revolves around the sun") is a true statement, \( \sim q \) becomes false. Therefore, the entire expression \( p \land \sim q \) is false.
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The symbol  means “and”.

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