Answer :
Final answer:
Using deductive reasoning and the principle of hypothetical syllogism, we can conclude that 'If Mr. Small turns 200 bowls, then he will raise the money for a new lathe.' This is because the two given premises logically lead to this conclusion.
Explanation:
When attempting to draw valid conclusions from a set of premises, it's important to consider the structure of the argument presented. In this case, we are given two conditional statements:
- If Mr. Small turns 200 bowls, then he will go to the Ann Arbor Art Fair.
- If Mr. Small goes to the Ann Arbor Art Fair, then he will raise the money for a new lathe.
By chaining these two conditional statements together, we can use deductive reasoning to draw a conclusion. This form of reasoning is sometimes referred to as hypothetical syllogism, where if 'A implies B' and 'B implies C', then 'A implies C'. Therefore:
- If Mr. Small turns 200 bowls, then he will go to the Ann Arbor Art Fair (given).
- If Mr. Small goes to the Ann Arbor Art Fair, then he will raise the money for a new lathe (given).
Combining these two statements, we arrive at the conclusion that:
- If Mr. Small turns 200 bowls, then he will raise the money for a new lathe. (valid conclusion)
Options 1, 2, and 3 do not follow deductive reasoning from the given premises, so they are not valid conclusions. Therefore, the correct answer is option 4.
