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The statement provided is:

\[
(\sim q \land p) \to (\sim p \lor q)
\]

We will construct the truth table for this logical expression step by step. Let’s break it down:

1. \( p \) and \( q \) are the two variables.
2. \( \sim q \land p \) is the conjunction of the negation of \( q \) and \( p \).
3. \( \sim p \lor q \) is the disjunction of the negation of \( p \) and \( q \).
4. Finally, the whole statement is the implication: \( (\sim q \land p) \to (\sim p \lor q) \).

We need to calculate each component and then the final implication. Here's how we organize the truth table:

| \( p \) | \( q \) | \( \sim p \) | \( \sim q \) | \( \sim q \land p \) | \( \sim p \lor q \) | \( (\sim q \land p) \to (\sim p \lor q) \) |
|--------|--------|--------------|--------------|--------------------|------------------|---------------------------------------|
| T      | T      | F            | F            | F                  | T                | T                                     |
| T      | F      | F            | T            | T                  | F                | F                                     |
| F      | T      | T            | F            | F                  | T                | T                                     |
| F      | F      | T            | T            | F                  | T                | T                                     |

### Explanation:

- \( \sim p \): Negation of \( p \)
- \( \sim q \): Negation of \( q \)
- \( \sim q \land p \): Conjunction of \( \sim q \) and \( p \)
- \( \sim p \lor q \): Disjunction of \( \sim p \) and \( q \)
- \( (\sim q \land p) \to (\sim p \lor q) \): The implication we are testing.

Would you like further clarification on any part of this table? Here are some related questions for further exploration:

1. What are the key differences between conjunction and disjunction in logic?
2. How does an implication work in truth tables?
3. What is the significance of negation in logical expressions?
4. How do truth values change in a biconditional statement compared to an implication?
5. What are some common mistakes when constructing truth tables?

**Tip**: Always break down complex logical expressions into smaller parts when constructing truth tables to avoid confusion.

This solution constructs a truth table for the logical statement (∼q ∧ p) → (∼p ∨ q), demonstrating the steps involved in breaking down and calculating each component of the expression.

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