QuestionTranslate the following argument into symbolic form. Then determine whether the argument is valid or invalid. The computer is thinking but the computer is not working. If the computer is working then the computer is thinking. Therefore, the computer is working.
Write the statement in symbolic form.

Studdy Solution

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, $W$

STEP 7

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.

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Studdy Solution

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, $W$

STEP 7

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Studdy Solution

STEP 1

1. Let T T T represent "The computer is thinking."2. Let W W 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∧¬W T \land \neg W T∧¬W.

STEP 4

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

STEP 5

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

STEP 6

Combine the premises and conclusion into a logical argument:1. T∧¬W T \land \neg W T∧¬W2. W→T W \rightarrow T W→T3. Therefore, W W W

STEP 7

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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.

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

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

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

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

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