https://file.aiquickdraw.com/mathbot/file/17275396269439y1cuz2r.jpg

The image contains the following problem in Indonesian:

**Problem:**
"7. Tuliskan tabel kebenaran dari setiap proposisi:"

This translates to:
"Write the truth table for each proposition:"

The propositions given are:

- a. \( (\neg p \vee q) \vee p \)
- b. \( (p \vee q) \land \neg p \)
- c. \( (p \vee q) \vee (\neg p \vee q) \)

I'll now create the truth tables for each of these propositions.Here are the truth tables for each proposition:

| \(p\)   | \(q\)   | \(\neg p\) | \(p \vee q\) | \(\neg p \vee q\) | \((\neg p \vee q) \vee p\) | \((p \vee q) \land \neg p\) | \((p \vee q) \vee (\neg p \vee q)\) |
|--------|--------|-----------|-------------|-----------------|-----------------------|-------------------------|--------------------------------|
| True   | True   | False     | True        | True            | True                  | False                   | True                           |
| True   | False  | False     | True        | False           | True                  | False                   | True                           |
| False  | True   | True      | True        | True            | True                  | True                    | True                           |
| False  | False  | True      | False       | True            | True                  | False                   | True                           |

### Explanation:

- **a. \( (\neg p \vee q) \vee p \)**: This evaluates to `True` for all combinations of \(p\) and \(q\).
- **b. \( (p \vee q) \land \neg p \)**: This is only `True` when \(p\) is `False` and \(q\) is `True`, meaning \(p\) must be false and \(q\) true for the conjunction to hold.
- **c. \( (p \vee q) \vee (\neg p \vee q) \)**: This evaluates to `True` for all combinations of \(p\) and \(q\).

Would you like further clarification on any specific part?

### Here are some related questions:
1. How is the negation of a proposition applied in a truth table?
2. Why does the disjunction \(p \vee q\) give `True` when either \(p\) or \(q\) is `True`?
3. Can you explain why the conjunction \(p \land q\) is only true when both are true?
4. How does the truth table change if additional logical operators are included?
5. Can you simplify the given propositions using logical identities?

### Tip:
Always start with the simplest logical components (like negation or disjunction) when constructing truth tables, then build up to more complex expressions.

Tuliskan tabel kebenaran dari setiap proposisi: a. (¬p ∨ q) ∨ p, b. (p ∨ q) ∧ ¬p, c. (p ∨ q) ∨ (¬p ∨ q)

Learn how to construct truth tables for propositional logic expressions, including examples of disjunction, conjunction, and negation. Suitable for students in undergraduate or high school logic courses.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation