Answer: Choice D
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Reason:
Let's go through the four answer choices to see which are true and which are false. We'll rule out the ones that are true.
- A) This is true. We can use inductive reasoning to form a conjecture. A conjecture is basically a generalized guess. For example, a guess would be something like "the sum of the first n odd numbers is n^2". So 1+3 = 4, 1+3+5 = 9, 1+3+5+7 = 16, 1+3+5+7+9 = 25, and so on. Does the pattern go on forever? Or does it stop at some point? That's why a proof is needed.
- B) This is true. See choice A.
- C) This is true. Some conjectures have been proven (such as the example I mentioned in choice A) while others have not. A famous unproven conjecture is Goldbach's Conjecture.
- D) This is false. Inductive reasoning helps form a conjecture, but it does not lead to definitive proof. We would need deductive reasoning.