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To construct the truth table for \((\neg q \land (p \rightarrow q)) \rightarrow \neg p\), let us break the logical expression into smaller components and evaluate them step by step.

### Logical Symbols:
- \(\neg\): NOT
- \(\land\): AND
- \(\rightarrow\): Implication

### Steps:
1. Define the variables \(p\) and \(q\).
2. Compute \(\neg q\) (NOT \(q\)).
3. Compute \(p \rightarrow q\) (Implication: true unless \(p\) is true and \(q\) is false).
4. Compute \(\neg q \land (p \rightarrow q)\) (AND operation between \(\neg q\) and \((p \rightarrow q)\)).
5. Compute \(\neg p\) (NOT \(p\)).
6. Compute \((\neg q \land (p \rightarrow q)) \rightarrow \neg p\).

Let’s construct the truth table:

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

### Explanation of Each Column:
1. \(p\) and \(q\) are the input truth values.
2. \(\neg q\): Flip the truth value of \(q\).
3. \(p \rightarrow q\): True unless \(p = T\) and \(q = F\).
4. \(\neg q \land (p \rightarrow q)\): True only when both \(\neg q\) and \((p \rightarrow q)\) are true.
5. \(\neg p\): Flip the truth value of \(p\).
6. \((\neg q \land (p \rightarrow q)) \rightarrow \neg p\): True unless \((\neg q \land (p \rightarrow q)) = T\) and \(\neg p = F\).

Would you like a detailed breakdown of any specific step? Let me know!  

### Related Questions:
1. What are the rules for logical implication (\(p \rightarrow q\)) in propositional logic?
2. How does the AND (\(\land\)) operation work in a truth table?
3. Can you explain the role of the NOT (\(\neg\)) operator in propositional logic?
4. Why is the statement \((p \rightarrow q)\) always true when \(p\) is false?
5. How do you analyze the logical equivalence of compound statements?

### Tip:
When working with logical expressions, break the problem into small parts and calculate each component step by step to avoid confusion.

Construct truth table for (~q∧(p → q)) → ~p

Explore the truth table construction for the logical expression (~q∧(p → q)) → ~p. This step-by-step solution covers key concepts in propositional logic, including negation, implication, and conjunction. Ideal for students in Grades 11-12 or undergraduate logic courses.

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