The logical form of the argument can be written as follows:

Let's denote:
P: The positive number is less than 2
Q: Its square is not larger than 4

The argument can then be written as:
1. If P, then Q (If the positive number is less than 2, then its square is not larger than 4)
2. If not Q, then not P (If square of number is larger than 4, then the number is not less than 2)
∴ Not P and Q (The positive number is not less than 2 and its square is not larger than 4)

Now, let's create a truth table to test the argument for validity:

| P | Q | If P, then Q | If not Q, then not P | Not P and Q |
|---|---|--------------|----------------------|-------------|
| T | T | T | T | F |
| T | F | F | F | F |
| F | T | T | T | T |
| F | F | T | T | F |

From the truth table, we can see that the argument is not valid. The conclusion (Not P and Q) is not true in all cases where the premises (If P, then Q and If not Q, then not P) are true.

Question

The logical form of the argument can be written as follows:

Let's denote:
P: The positive number is less than 2
Q: Its square is not larger than 4

The argument can then be written as:
1. If P, then Q (If the positive number is less than 2, then its square is not larger than 4)
2. If not Q, then not P (If square of number is larger than 4, then the number is not less than 2)
∴ Not P and Q (The positive number is not less than 2 and its square is not larger than 4)

Now, let's create a truth table to test the argument for validity:

| P | Q | If P, then Q | If not Q, then not P | Not P and Q |
|---|---|--------------|----------------------|-------------|
| T | T | T            | T                    | F           |
| T | F | F            | F                    | F           |
| F | T | T            | T                    | T           |
| F | F | T            | T                    | F           |

From the truth table, we can see that the argument is not valid. The conclusion (Not P and Q) is not true in all cases where the premises (If P, then Q and If not Q, then not P) are true.

Knowee AI · Accepted Answer

The logical form of the argument can be written as follows:

Let's denote:
P: The positive number is less than 2
Q: Its square is not larger than 4

The argument can then be written as:
1. If P, then Q (If the positive number is less than 2, then its square is not larger than 4)
2. If not Q, then not P (If square of number is larger than 4, then the number is not less than 2)
∴ Not P and Q (The positive number is not less than 2 and its square is not larger than 4)

Now, let's create a truth table to test the argument for validity:

| P | Q | If P, then Q | If not Q, then not P | Not P and Q |
|---|---|--------------|----------------------|-------------|
| T | T | T            | T                    | F           |
| T | F | F            | F                    | F           |
| F | T | T            | T                    | T           |
| F | F | T            | T                    | F           |

From the truth table, we can see that the argument is not valid. The conclusion (Not P and Q) is not true in all cases where the premises (If P, then Q and If not Q, then not P) are true.

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