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Examine the following reasoning: “If the sky is overcast tonight, then it will rain tomorrow; and if it rains tomorrow, I will be on leave the next day. Therefore, if the sky is overcast tonight, I will be on leave the next day.”

1. Statement 1: The argument given is valid. Statement 2: For three statements p, q and r, if p⇒q and q⇒r, then p⇒r.
2. Statement 1: The argument given is valid. Statement 2: For three statements p, q and r, if p⇒q and q⇒r, then p⇒r.
3. Statement 1: The argument given is valid. Statement 2: For three statements p, q and r, if p⇒q and q⇒r, then p⇒r.
4. Statement 1: The argument given is valid. Statement 2: For three statements p, q and r, if p⇒q and q⇒r, then p⇒r.

Correct answer: Statement 1: The argument given is valid. Statement 2: For three statements p, q and r, if p⇒q and q⇒r, then p⇒r.

Solution

The argument is valid because it follows the logical structure of transitive reasoning, where if the first condition leads to a second, and the second leads to a third, then the first condition must lead to the third.

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