Math Snap

STEP 1

1. Let $T$ represent "The computer is thinking."
2. Let $W$ represent "The computer is working."
3. We need to translate the argument into symbolic form and determine its validity.

STEP 2

1. Translate each statement into symbolic form.
2. Analyze the logical structure of the argument.
3. Determine the validity of the argument.

STEP 3

Translate the first statement: "The computer is thinking but the computer is not working."
This can be written as: $T \land \neg W$.

STEP 4

Translate the second statement: "If the computer is working then the computer is thinking."
This can be written as: $W \rightarrow T$.

STEP 5

Translate the conclusion: "Therefore, the computer is working."
This can be written as: $W$.

STEP 6

Combine the premises and conclusion into a logical argument:
1. $T \land \neg W$
2. $W \rightarrow T$
3. Therefore, $W$

To determine the validity, we need to check if the conclusion $W$ logically follows from the premises $T \land \neg W$ and $W \rightarrow T$.
The premises $T \land \neg W$ indicate that the computer is thinking but not working, which contradicts the conclusion $W$.
The argument is invalid because the conclusion $W$ does not logically follow from the premises. The premises actually contradict the conclusion.