Let's tackle these two problems step by step. We will construct the truth tables for both compound statements as required.

1. Construct a truth table for the compound statement $\neg(p \land q) \leftrightarrow (\neg p \lor \neg q)$.

This is a biconditional statement. The first part is $\neg(p \land q)$, and the second part is $\neg p \lor \neg q$. The table will compare these two parts and check if they are logically equivalent (i.e., whether the entire expression is true or false).

Truth Table Construction:

Conclusion: Since the final column has all true values, this compound statement is a tautology.

2. Construct a truth table for the compound statement $(p \land \neg q) \rightarrow (p \rightarrow q)$.

Here, we first need to compute $p \land \neg q$ and $p \rightarrow q$ before considering the implication $(p \land \neg q) \rightarrow (p \rightarrow q)$.

Truth Table Construction:

Conclusion: Since the final column has a mix of true and false values, this compound statement is a contingency.

Let me know if you'd like further clarification or details on these steps. Here are some additional questions you can explore:

1. How would the truth table change if we modified $\lor$ to $\land$ in the first statement?
2. What logical operation can you infer from $\leftrightarrow$?
3. How would you define a contradiction based on the truth table outcomes?
4. Why is the second statement not a tautology or contradiction?
5. What role do negations play in these logical expressions?

Tip: When constructing truth tables, always calculate the intermediate steps carefully to ensure accurate results.