If there is a valid conclusion, which is it?

1) No conclusion possible
2) If Mr. Small raises the money for a new lathe, then he will have turned 200 bowls.
3) Mr. Small enters the Ann Arbor Art Fair; therefore, he gets a new lathe.
4) If Mr. Small turns 200 bowls, then he will raise the money for a new lathe.

Question

03-05-2025
Mathematics

High School

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If there is a valid conclusion, which is it?

1) No conclusion possible
2) If Mr. Small raises the money for a new lathe, then he will have turned 200 bowls.
3) Mr. Small enters the Ann Arbor Art Fair; therefore, he gets a new lathe.
4) If Mr. Small turns 200 bowls, then he will raise the money for a new lathe.

Answer :

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MariaRobell MariaRobell · Answer 1 · 2024-03-08T05:19:30-05:00

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.