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To solve the problem, we'll construct a truth table for the logical statement:

\[
[(p \rightarrow (q \lor r)) \iff (p \land \neg q)] \rightarrow r
\]

### Step 1: Break Down the Statement
The statement consists of several components:
1. \( p \rightarrow (q \lor r) \)
2. \( p \land \neg q \)
3. \( (p \rightarrow (q \lor r)) \iff (p \land \neg q) \)
4. \( [(p \rightarrow (q \lor r)) \iff (p \land \neg q)] \rightarrow r \)

### Step 2: Construct the Truth Table
We'll create a truth table that includes all intermediate components to evaluate the final expression.

| \(p\) | \(q\) | \(r\) | \(q \lor r\) | \(\neg q\) | \(p \rightarrow (q \lor r)\) | \(p \land \neg q\) | \((p \rightarrow (q \lor r)) \iff (p \land \neg q)\) | \([(p \rightarrow (q \lor r)) \iff (p \land \neg q)] \rightarrow r\) |
|:-----:|:-----:|:-----:|:------------:|:---------:|:--------------------------:|:-----------------:|:-----------------------------------------------:|:------------------------------------------------------------------:|
|   T   |   T   |   T   |      T       |     F     |              T             |         F         |                       F                       |                                 T                                  |
|   T   |   T   |   F   |      T       |     F     |              T             |         F         |                       F                       |                                 T                                  |
|   T   |   F   |   T   |      T       |     T     |              T             |         T         |                       T                       |                                 T                                  |
|   T   |   F   |   F   |      F       |     T     |              F             |         T         |                       F                       |                                 T                                  |
|   F   |   T   |   T   |      T       |     F     |              T             |         F         |                       T                       |                                 T                                  |
|   F   |   T   |   F   |      T       |     F     |              T             |         F         |                       T                       |                                 F                                  |
|   F   |   F   |   T   |      T       |     T     |              T             |         F         |                       T                       |                                 T                                  |
|   F   |   F   |   F   |      F       |     T     |              T             |         F         |                       T                       |                                 F                                  |

### Step 3: Analyze the Final Column
The final column of the truth table represents the entire expression \([(p \rightarrow (q \lor r)) \iff (p \land \neg q)] \rightarrow r\).

- For all possible truth values of \(p\), \(q\), and \(r\), the final expression is **not** always true. Specifically, the expression is false in some cases.

### Conclusion
The given statement \([(p \rightarrow (q \lor r)) \iff (p \land \neg q)] \rightarrow r\) is **not a tautology**.

Would you like any further details or explanations? 

### Relative Questions:
1. What is a tautology, and how is it different from a contradiction?
2. How can logical equivalences simplify complex logical statements?
3. What are some practical applications of truth tables in computer science?
4. How does the logical operator "iff" (if and only if) work in logical statements?
5. What are some common pitfalls when constructing truth tables for logical expressions?

### Tip:
When constructing truth tables, always carefully evaluate each component of the expression step by step to avoid errors, especially with more complex statements.

Explore how to solve a complex logical statement using truth tables. Step-by-step breakdown and analysis of [(p → (q ∨ r)) ↔ (p ∧ ¬q)] → r. Suitable for advanced high school students and anyone interested in logic and truth tables.

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