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The problem asks to convert the argument into symbolic form and then use a truth table to determine its validity.

### Step 1: Convert the statements into logical symbols.
From the problem:

- \( P \): "Elephant is angry"
- \( Q \): "Elephant smirks"
- \( R \): "Chicken is frightened"

### The argument:
1. "If the elephant is angry, the chicken is frightened."  
   This translates to:  
   \[
   P \to R
   \]
2. "The chicken is frightened and the elephant smirks."  
   This is:  
   \[
   R \land Q
   \]
3. Conclusion: "So, the elephant is angry."  
   This is:  
   \[
   P
   \]

### Logical structure of the argument:
Premises:
1. \( P \to R \)
2. \( R \land Q \)

Conclusion:
- \( P \)

### Step 2: Construct a truth table.

We'll build a truth table using the variables \( P \), \( Q \), and \( R \), and check the validity of the argument.

| \( P \) | \( Q \) | \( R \) | \( P \to R \) | \( R \land Q \) | Conclusion \( P \) |
|--------|--------|--------|--------------|--------------|--------------------|
| T      | T      | T      | T            | T            | T                  |
| T      | T      | F      | F            | F            | T                  |
| T      | F      | T      | T            | F            | T                  |
| T      | F      | F      | F            | F            | T                  |
| F      | T      | T      | T            | T            | F                  |
| F      | T      | F      | T            | F            | F                  |
| F      | F      | T      | T            | F            | F                  |
| F      | F      | F      | T            | F            | F                  |

### Step 3: Analyze the validity.
An argument is valid if whenever all premises are true, the conclusion is also true. 

- Rows 1 and 5 are the only rows where both premises are true: \( P \to R \) is true, and \( R \land Q \) is true.
- In row 1, the conclusion \( P \) is true.
- In row 5, the conclusion \( P \) is false.

Since there is a row (row 5) where both premises are true and the conclusion is false, **the argument is invalid**.

Would you like a deeper explanation of the truth table, or do you have other questions?

### Related Questions:
1. What does it mean when an argument is valid in logic?
2. How is the truth value of \( P \to R \) determined in a truth table?
3. Can you explain the difference between validity and soundness in logical arguments?
4. What are some examples of common logical fallacies that lead to invalid arguments?
5. How can truth tables be used to determine logical equivalence between statements?

### Tip:
When constructing a truth table, always ensure all possible combinations of truth values are covered for each variable involved.

If the elephant is angry, the chicken is frightened. The chicken is frightened and the elephant smirks. Therefore, the elephant is angry.

This logic problem uses a truth table to determine the validity of an argument involving an elephant, chicken, and their emotions. Learn how to assess the truth values of conditional statements and conjunctions. Suitable for students in Grades 9-12.

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