If pp is true and qq is true, find the truth value of:
\neg, p, or, \neg, q
¬p∨¬q

Given that both \( p \) and \( q \) are true, let's evaluate the expression \( \neg p \lor \neg q \).

### Step 1: Determine the truth values of \( \neg p \) and \( \neg q \).
- Since \( p \) is true, \( \neg p \) (not \( p \)) is false.
- Since \( q \) is true, \( \neg q \) (not \( q \)) is false.

### Step 2: Evaluate \( \neg p \lor \neg q \).
- The logical OR ( \( \lor \) ) operation between two statements is true if at least one of the statements is true. In this case:
  \[
  \neg p \lor \neg q = \text{false} \lor \text{false} = \text{false}
  \]

### Conclusion
The truth value of \( \neg p \lor \neg q \) is **false**.

Would you like more details or have any questions? 

Here are some related questions:

1. What is the truth value of \( \neg p \land q \) if \( p \) is false and \( q \) is true?
2. How do truth tables help in determining the truth value of logical expressions?
3. What is the difference between the logical operations AND (\( \land \)) and OR (\( \lor \))?
4. Can a compound statement involving OR (\( \lor \)) ever be false?
5. How does the truth value of \( p \lor q \) change if one of the statements is false?

**Tip:** Remember, in logical operations, "not" (\( \neg \)) simply flips the truth value of a statement.

Learn how to evaluate the logical expression \( \neg p \lor \neg q \) when \( p \) and \( q \) are both true. This problem involves Boolean algebra and logical operations, exploring how the truth values of \( p \) and \( q \) affect the outcome of a logical OR operation.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation