Question 1174481
Let's break down this argument into propositional logic and use a truth table to determine its validity.

**1. Define Propositions:**

* **P:** A polygon is regular.
* **Q:** A polygon has a side which is longer than another side of the polygon.
* **R:** All the sides of the polygon are congruent.
* **S:** An interior angle of the polygon has a measure greater than one of the interior angles of the polygon.

**2. Express the Argument in Symbolic Form:**

* Premise 1: P ∨ Q
* Premise 2: P → R
* Premise 3: Q → S
* Conclusion: R ∨ S

**3. Construct the Truth Table:**

We need to consider all possible combinations of truth values for P, Q, R, and S.

| P | Q | R | S | P ∨ Q | P → R | Q → S | R ∨ S |
|---|---|---|---|-------|-------|-------|-------|
| T | T | T | T | T     | T     | T     | T     |
| T | T | T | F | T     | T     | F     | T     |
| T | F | T | T | T     | T     | T     | T     |
| T | F | T | F | T     | T     | T     | T     |
| F | T | F | T | T     | T     | T     | T     |
| F | T | F | F | T     | T     | F     | F     |
| F | F | F | T | F     | T     | T     | T     |
| F | F | F | F | F     | T     | T     | F     |

**4. Evaluate the Argument:**

To determine validity, we need to check if the conclusion (R ∨ S) is true whenever all the premises (P ∨ Q, P → R, Q → S) are true.

Let's examine the rows where all premises are true:

* **Row 1:** P, Q, R, S are all true. All premises and the conclusion are true.
* **Row 3:** P, R, S are true; Q is false. All premises and the conclusion are true.
* **Row 4:** P, R are true; Q, S are false. All premises and the conclusion are true.
* **Row 5:** Q, S are true; P, R are false. All premises and the conclusion are true.
* **Row 7:** S is true; P, Q, R are false. Premise 2 and 3 are true because the antecedent is false. Premise 1 is false. The conclusion is true.
* **Row 8:** All are false. Premise 2, and 3 are true because the antecedent is false. Premise 1 is false. The conclusion is false.

Let's adjust the table to show the combined premises. We only care about rows where all premises are true.

| P | Q | R | S | P ∨ Q | P → R | Q → S | (P ∨ Q) ∧ (P → R) ∧ (Q → S) | R ∨ S |
|---|---|---|---|-------|-------|-------|-------------------------------|-------|
| T | T | T | T | T     | T     | T     | T                             | T     |
| T | F | T | T | T     | T     | T     | T                             | T     |
| T | F | T | F | T     | T     | T     | T                             | T     |
| F | T | F | T | T     | T     | T     | T                             | T     |
| F | F | F | T | F     | T     | T     | F                             | T     |
| F | F | F | F | F     | T     | T     | F                             | F     |
| F | T | F | F | T     | T     | F     | F                             | F     |
| T | T | T | F | T     | T     | F     | F                             | T     |

In every row where all premises are true, the conclusion is also true. Therefore, the argument is valid.