Is this a valid argument?

Question

Given: If an object is in the shape of a sphere, then it rolls.

This ball is in the shape of a sphere.

Conclusion: This ball rolls.

Yes. This argument uses the Law of Syllogism.

Yes. This argument uses the Law of Detachment.

No. This is an improper use of the Law of Syllogism.

No. This is an improper use of the Law of Detachment.

Answer 1

The argument you provided is valid and correctly applies the Law of Detachment.

The argument is structured as follows:

1. Given: If an object is in the shape of a sphere, then it rolls. (This is a conditional statement: If P, then Q)
2. Premise: This ball is in the shape of a sphere. (This is P)
3. Conclusion: This ball rolls. (This is Q)

Since the first premise states that if something is spherical, it will roll (If P then Q), and the second premise confirms that the ball is indeed spherical (P), we can validly conclude that this ball rolls (Q).

Therefore, the correct answer is: Yes. This argument uses the Law of Detachment.