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 Detachment.

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

Yes. This argument uses the Law of Syllogism.

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

Answer 1

Yes. This argument uses the Law of Detachment.

In this argument, the first statement is a conditional statement (if-then) where the hypothesis is "an object is in the shape of a sphere" and the conclusion is "it rolls." Since the second statement affirms the hypothesis ("this ball is in the shape of a sphere"), we can apply the Law of Detachment to conclude that the conclusion ("this ball rolls") is valid.