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To complete this truth table, let’s analyze each expression step-by-step. Here’s a breakdown of the symbols and operations involved:

1. **p XOR q ( \( p \oplus q \) )**: This is true if and only if \( p \) and \( q \) have different truth values.
2. **p XOR NOT q ( \( p \oplus \sim q \) )**: This is true if and only if \( p \) and \( \sim q \) have different truth values.
3. **( \( p \oplus q \) ) OR ( \( p \oplus \sim q \) )**: This expression is true if either \( p \oplus q \) or \( p \oplus \sim q \) is true.
4. **( \( p \oplus q \) ) AND ( \( p \oplus \sim q \) )**: This expression is true only if both \( p \oplus q \) and \( p \oplus \sim q \) are true.

Let’s evaluate these for each combination of \( p \) and \( q \) values (T = True, F = False):

### Step-by-Step Evaluation:

| p | q | \( p \oplus q \) | \( p \oplus \sim q \) | \( (p \oplus q) \lor (p \oplus \sim q) \) | \( (p \oplus q) \land (p \oplus \sim q) \) |
|---|---|-----------------|-----------------------|------------------------------------------|-------------------------------------------|
| T | T | F               | T                     | T                                        | F                                         |
| T | F | T               | T                     | T                                        | T                                         |
| F | T | T               | F                     | T                                        | F                                         |
| F | F | F               | F                     | F                                        | F                                         |

### Solution for Each Row:

1. **Row 1**: \( p = T \), \( q = T \)
   - \( p \oplus q = F \)
   - \( p \oplus \sim q = T \)
   - \( (p \oplus q) \lor (p \oplus \sim q) = T \)
   - \( (p \oplus q) \land (p \oplus \sim q) = F \)

2. **Row 2**: \( p = T \), \( q = F \)
   - \( p \oplus q = T \)
   - \( p \oplus \sim q = T \)
   - \( (p \oplus q) \lor (p \oplus \sim q) = T \)
   - \( (p \oplus q) \land (p \oplus \sim q) = T \)

3. **Row 3**: \( p = F \), \( q = T \)
   - \( p \oplus q = T \)
   - \( p \oplus \sim q = F \)
   - \( (p \oplus q) \lor (p \oplus \sim q) = T \)
   - \( (p \oplus q) \land (p \oplus \sim q) = F \)

4. **Row 4**: \( p = F \), \( q = F \)
   - \( p \oplus q = F \)
   - \( p \oplus \sim q = F \)
   - \( (p \oplus q) \lor (p \oplus \sim q) = F \)
   - \( (p \oplus q) \land (p \oplus \sim q) = F \)

Would you like further details on any step or concept?

### Related Questions:
1. What is the difference between XOR and AND operators in Boolean logic?
2. How do truth tables help in understanding logical expressions?
3. Why is \( p \oplus q \) true only when \( p \) and \( q \) are different?
4. How would this table look if we used NOR and NAND instead of OR and AND?
5. What practical applications use XOR operations?

### Tip:
When analyzing truth tables, break down complex expressions step-by-step to understand each intermediate result before combining them.

Complete the following truth table by filling in the blanks with T or F as appropriate for the logical expressions involving XOR and NOT operations.

Learn how to complete a truth table involving XOR and NOT operations. This example demonstrates step-by-step evaluations of Boolean expressions, such as p XOR q and p XOR NOT q, to determine truth values for OR and AND combinations. Suitable for Grades 10-12.

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