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The image you've uploaded contains a problem asking to determine the type of the given logical formulas using equivalence rules.

### Problem Overview:
The problem appears to provide three logical formulas, and the task is to judge their type, likely identifying whether they are tautologies, contradictions, or contingent statements based on their logical structure.

The formulas provided are:
1. \( \neg(p \land q \rightarrow q) \)
2. \( (p \rightarrow (p \lor q)) \lor (p \rightarrow r) \)
3. \( (p \lor q) \rightarrow (p \land r) \)

### Analyzing the Formulas:

1. **Formula 1**: \( \neg(p \land q \rightarrow q) \)
   - The expression inside the negation is \( p \land q \rightarrow q \). This implication states that if \( p \land q \) is true, then \( q \) must be true. This is trivially true since \( p \land q \) implies \( q \).
   - Therefore, \( p \land q \rightarrow q \) is a tautology.
   - The negation of a tautology is a contradiction. 
   - So, \( \neg(p \land q \rightarrow q) \) is a **contradiction**.

2. **Formula 2**: \( (p \rightarrow (p \lor q)) \lor (p \rightarrow r) \)
   - The expression \( p \rightarrow (p \lor q) \) is always true (tautology) because if \( p \) is true, \( p \lor q \) is also true.
   - \( (p \rightarrow r) \) is also a tautology since it's true unless \( p \) is true and \( r \) is false.
   - A disjunction where at least one component is a tautology results in a tautology.
   - So, \( (p \rightarrow (p \lor q)) \lor (p \rightarrow r) \) is a **tautology**.

3. **Formula 3**: \( (p \lor q) \rightarrow (p \land r) \)
   - This expression suggests that if \( p \lor q \) is true, then \( p \land r \) should be true.
   - This is not generally true since \( p \lor q \) being true does not guarantee that both \( p \) and \( r \) are true.
   - Therefore, \( (p \lor q) \rightarrow (p \land r) \) is **not a tautology**. Its truth value depends on specific values of \( p \), \( q \), and \( r \), making it a **contingent statement**.

### Summary:
1. \( \neg(p \land q \rightarrow q) \) is a **contradiction**.
2. \( (p \rightarrow (p \lor q)) \lor (p \rightarrow r) \) is a **tautology**.
3. \( (p \lor q) \rightarrow (p \land r) \) is a **contingent statement**.

Would you like more details on how these conclusions are reached or have any questions?

### Related Questions:
1. What is the definition of a tautology in propositional logic?
2. How can you prove that a formula is a contradiction using truth tables?
3. What are the basic equivalence laws used in propositional logic?
4. How does the concept of contingent statements differ from tautologies and contradictions?
5. What role does the material implication play in determining the type of logical statements?

### Tip:
When working with logical formulas, constructing a truth table can help you determine whether the formula is a tautology, contradiction, or contingent.

用等值演算法判断下列公式的类型：
(1) ¬(p ∧ q → q)
(2) (p → (p ∨ q)) ∨ (p → r)
(3) (p ∨ q) → (p ∧ r)

Analyze and determine the type of the given logical formulas using equivalence rules. Explore concepts in propositional logic, including tautologies, contradictions, and contingent statements.

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