https://file.aiquickdraw.com/mathbot/file/1728354590695t53w2ieh.jpg

Let's evaluate the logical expressions in the image.

### Question 1:
Logical expression:  
\[ \text{NOT} \left( (5 > 3) \text{ OR } (6 < 10) \right) \]

1. **Evaluate the inner expressions:**
   - \( 5 > 3 \) is **True**.
   - \( 6 < 10 \) is **True**.

2. **OR operator:**
   - \( \text{True} \text{ OR } \text{True} \) is **True**.

3. **Apply the NOT operator:**
   - \( \text{NOT True} \) is **False**.

Thus, the statement evaluates to **False**, and the selected answer is correct.

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### Question 2:
Logical expression:  
\[ \left( (2 + 2 = 5) \text{ OR } (8 > 5) \right) \text{ AND } \text{NOT} (10 > 5) \]

1. **Evaluate the inner expressions:**
   - \( 2 + 2 = 5 \) is **False**.
   - \( 8 > 5 \) is **True**.
   - \( 10 > 5 \) is **True**.

2. **OR operator:**
   - \( \text{False} \text{ OR } \text{True} \) is **True**.

3. **NOT operator on \( 10 > 5 \):**
   - \( \text{NOT True} \) is **False**.

4. **AND operator:**
   - \( \text{True} \text{ AND } \text{False} \) is **False**.

Thus, the statement evaluates to **False**, but the selected answer is **True**, which is incorrect.

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Would you like more details or further clarifications? Here are 5 follow-up questions:

1. What is the difference between the AND and OR logical operators?
2. How does the NOT operator affect a logical expression?
3. Can you combine more than two logical operators in one expression?
4. Why does \( (2 + 2 = 5) \) evaluate to False in logical operations?
5. How can De Morgan’s laws be applied to simplify logical expressions?

**Tip:** Always evaluate inner expressions first when working with complex logical statements, then apply operators like AND, OR, and NOT.

Evaluate the following logical expression: NOT ((5 > 3) OR (6 < 10)). Is this True or False?

Learn how to evaluate logical expressions using NOT, AND, OR operators in Boolean Algebra. This problem walks through the steps for evaluating expressions and applying De Morgan's laws. Suitable for students in Grades 9-12.

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