https://file.aiquickdraw.com/mathbot/file/1727418545037szmdmqxv.jpg

make just the table and dont print any thing else just the table using T and F

Here's the truth table as requested:

| p | q | ¬p | ¬q | ¬p ∧ ¬q | p ∧ q | p ∨ (¬p ∧ ¬q) | p ∨ (¬p ∧ ¬q) ∨ (p ∧ q) |
|---|---|----|----|---------|-------|---------------|-------------------------|
| T | T | F  | F  | F       | T     | T             | T                       |
| T | F | F  | T  | F       | F     | T             | T                       |
| F | T | T  | F  | F       | F     | F             | F                       |
| F | F | T  | T  | T       | F     | T             | T                       |

If you have any questions or want more details, let me know!

### Related Questions:
1. How can we simplify expressions using Boolean algebra?
2. What are the common laws used in logical expressions?
3. What is the significance of a truth table in logical proofs?
4. How do we construct a truth table for more complex expressions?
5. Can we represent these logical expressions using Venn diagrams?

**Tip**: When building truth tables, ensure every possible combination of truth values for the variables is covered for accurate results.

Prove that p ∨ (¬p ∧ ¬q) ∨ (p ∧ q) = p ∨ (¬p ∧ ¬q)

Explore the step-by-step proof of the logical equivalence p ∨ (¬p ∧ ¬q) ∨ (p ∧ q) = p ∨ (¬p ∧ ¬q) using Boolean algebra. This solution includes a truth table breakdown and demonstrates key theorems like De Morgan's Law and the Idempotent Law.

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