Is this a valid argument?

Question

Given: If it is autumn, the leaves will fall off the trees.

If the leaves fall off the trees, I will have to pick up leaves.

Conclusion: If it is autumn, I will have to pick up leaves.

Yes. This argument uses the Law of Syllogism.

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

Yes. This argument uses the Law of Detachment.

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

Answer 1

The argument you presented is indeed valid, and it utilizes the Law of Syllogism correctly. Here's the reasoning:

1. The first premise states: If it is autumn, then the leaves will fall off the trees.
2. The second premise states: If the leaves fall off the trees, then I will have to pick up leaves.
3. The conclusion drawn is: If it is autumn, then I will have to pick up leaves.

According to the Law of Syllogism, if we have two conditional statements where the conclusion of the first becomes the hypothesis of the second, we can conclude a new conditional statement.

Therefore, the conclusion is valid, leading to the answer:

Yes. This argument uses the Law of Syllogism.