To translate the argument into symbolic form, we will use the following symbols:

• $p$: "Now you made orange."
• $q$: "Now you need to mix yellow."

The argument in English:

1. "You made orange or you need to mix yellow."
   This can be represented as:
   $p \lor q$ (This is a disjunction, "or").

2. "Now you need to mix yellow."
   This is just:
   $q$ (This is a simple statement).

3. "Now you did not make orange."
   This can be represented as:
   $\neg p$ (This is the negation of $p$).

The symbolic form of the argument:

1. $p \lor q$ (You made orange or you need to mix yellow)
2. $q$ (You need to mix yellow)
3. $\neg p$ (You did not make orange)

The structure of the argument:

• The argument has the form:
  • Premise 1: $p \lor q$
  • Premise 2: $q$
  • Conclusion: $\neg p$

To determine if the argument is valid, let's analyze the logical form:

We can use the rules of inference, specifically Disjunctive Syllogism, which states:

• If we have $p \lor q$ and $\neg p$, we can conclude $q$.

However, the second premise is simply $q$, not $\neg p$. This means we cannot directly apply Disjunctive Syllogism because we are not given $\neg p$ explicitly before concluding $\neg p$.

Is the argument valid or invalid?

Let's test it using a truth table:

$p$	$q$	$p \lor q$	$\neg p$
T	T	T	F
T	F	T	F
F	T	T	T
F	F	F	T

For the argument to be valid, whenever the premises are true, the conclusion must also be true. Let's check:

• Case 1: If $p$ is true and $q$ is true, then $p \lor q$ is true, but $\neg p$ is false, so the conclusion doesn't follow.
• Case 2: If $p$ is true and $q$ is false, then $p \lor q$ is true, but the conclusion is again false, so the argument does not follow in this case either.

Therefore, the argument is invalid.

Final answer:

• A. The argument is invalid. In symbolic form, the argument is:
  $(p \lor q), q \vdash \neg p$.

Let me know if you'd like further clarification or more examples. Here are some related questions:

1. How can we improve the argument to make it valid?
2. What is the difference between Disjunctive Syllogism and Modus Tollens?
3. Can you provide another example of an invalid argument and analyze it?
4. How do truth tables help in determining the validity of an argument?
5. What is the difference between a valid argument and a sound argument?

Tip: When working with logical arguments, always start by identifying the premises and conclusion clearly, then use truth tables or inference rules to test the validity.