Final answer:
Using the Law of Syllogism, it is possible to conclude that if one goes camping, then extra batteries will be needed. This law is used because the conclusion of one statement is the hypothesis of the next statement in the logical chain.
Step-by-step explanation:
To determine if a valid conclusion can be reached from the two true statements using the Law of Detachment or the Law of Syllogism, we examine the form of the statements given:
1. If I go camping, then I will need a flashlight. (Statement 1)
2. If I need a flashlight, then you will need extra batteries. (Statement 2)
The given statements suggest a chain of reasoning: going camping leads to needing a flashlight, and needing a flashlight leads to needing extra batteries. The Law of Syllogism can be applied here as it deals with hypothetical ("if-then") statements arranged in a chain where the conclusion of one statement is the hypothesis of the next. Applying the Law of Syllogism to the given statements, we can conclude:
If I go camping, then you will need extra batteries. (Valid conclusion)
The Law of Syllogism is the law that was used to reach this conclusion.