Answer the following questions
Examine whether the statement pattern is a tautology, contradiction or contingency
`(p ^^ ~q) rarr (~p ^^ ~q)`

Answer

To determine whether the statement pattern \((p \land \neg q) \rightarrow (\neg p \land \neg q)\) is a tautology, contradiction, or contingency, we will create a truth table.

### Step-by-Step Solution:

1. **Identify Variables**:
We have two variables \(p\) and \(q\).

2. **List Possible Truth Values**:
Each variable can be either true (T) or false (F). Therefore, we will have the following combinations:
- \(p = T, q = T\)
- \(p = T, q = F\)
- \(p = F, q = T\)
- \(p = F, q = F\)

3. **Calculate Negations**:
- \(\neg p\) (not \(p\))
- \(\neg q\) (not \(q\))

4. **Calculate Intermediate Expressions**:
- Calculate \(p \land \neg q\)
- Calculate \(\neg p \land \neg q\)

5. **Calculate the Final Expression**:
- Calculate \((p \land \neg q) \rightarrow (\neg p \land \neg q)\)

6. **Construct the Truth Table**:

| \(p\) | \(q\) | \(\neg p\) | \(\neg q\) | \(p \land \neg q\) | \(\neg p \land \neg q\) | \((p \land \neg q) \rightarrow (\neg p \land \neg q)\) |
|-------|-------|------------|------------|---------------------|--------------------------|--------------------------------------------------------|
| T | T | F | F | F | F | T |
| T | F | F | T | T | F | F |
| F | T | T | F | F | F | T |
| F | F | T | T | F | T | T |

7. **Analyze the Final Column**:
- The final column shows the truth values of the expression \((p \land \neg q) \rightarrow (\neg p \land \neg q)\).
- The values are: T, F, T, T.

8. **Conclusion**:
- Since the expression is not always true (there is at least one F) and not always false (there are T's), the statement is a **contingency**.

### Final Answer:
The statement pattern \((p \land \neg q) \rightarrow (\neg p \land \neg q)\) is a **contingency**.