Questions: Translate each argument into symbolic form. Then determine whether the argument is valid or invalid. You may use a truth table or, if applicable, compare the argument's symbolic form to standard valid or invalid form. (You can ignore differences in past, present, and future tense.) If he knows the material, he will do poorly. He will do well. He does not know the material. Let p be the statement "he knows the material," and q be the statement "he will do well." A. The argument is valid. In symbolic form, the argument is . B. The argument is invalid. In symbolic form, the argument is .

To translate the argument into symbolic form, we first identify the statements and their corresponding symbols:

• Let \( p \) be the statement "he knows the material."
• Let \( q \) be the statement "he will do well."

The argument given is:

1. If he knows the material, he will do poorly.
2. He will do well.
3. He does not know the material.

We need to express these statements symbolically:

1. "If he knows the material, he will do poorly" can be translated to: \( p \rightarrow \neg q \).
2. "He will do well" is: \( q \).
3. "He does not know the material" is: \( \neg p \).

Now, let's analyze the argument:

• Premise 1: \( p \rightarrow \neg q \)
• Premise 2: \( q \)
• Conclusion: \( \neg p \)

To determine if the argument is valid, we can use a truth table or compare it to known valid argument forms. Here, we'll use a truth table:

| \( p \) | \( q \) | \( \neg q \) | \( p \rightarrow \neg q \) | \( \neg p \) | |---------|---------|--------------|----------------------------|--------------| | T | T | F | F | F | | T | F | T | T | F | | F | T | F | T | T | | F | F | T | T | T |

We are interested in the rows where both premises are true:

• In the third row, \( p \rightarrow \neg q \) is true, and \( q \) is true. However, \( \neg p \) is also true, which matches the conclusion.

Since there is a row where both premises are true and the conclusion is also true, the argument is valid.

In summary, the argument is valid. The symbolic form of the argument is:

1. \( p \rightarrow \neg q \)
2. \( q \)
3. Therefore, \( \neg p \)