SOLUTION: National University: Mathematics in the Modern World ... - Free Printable

Problem Analysis:

The task requires identifying whether each statement uses inductive reasoning or deductive reasoning. Here's a brief explanation of the two types of reasoning:

1. Inductive Reasoning: This involves making broad generalizations from specific observations or patterns. It moves from specific instances to a general conclusion.
2. Deductive Reasoning: This involves drawing specific conclusions from general principles or premises. It moves from general statements to specific conclusions.

Solution:

Let's analyze each statement and determine whether it uses inductive or deductive reasoning.

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#### 1. I got up at nine o'clock for the past week. I will get up at nine o'clock tomorrow.
- Reasoning Type: Inductive
- Explanation: The conclusion is based on a pattern observed over the past week (specific instances). The expectation that the same pattern will continue is an inductive leap.

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#### 2. James Cameron’s last three movies were successful. His next movie will be successful.
- Reasoning Type: Inductive
- Explanation: The conclusion is based on the success of previous movies (specific instances). The assumption that the next movie will also be successful is an inductive generalization.

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#### 3. All even numbers are divisible by 2. The number 4 is even. Therefore, the number 4 is divisible by 2.
- Reasoning Type: Deductive
- Explanation: The conclusion is derived directly from the given premises (general principle: all even numbers are divisible by 2; specific instance: 4 is even). This is a logical deduction.

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#### 4. Every year since 1980, the United States has had a President. In 2023, the United States will have a President.
- Reasoning Type: Deductive
- Explanation: The conclusion is based on a general rule (the U.S. has had a President every year since 1980) applied to a specific instance (the year 2023). This is a logical deduction.

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#### 5. In this sequence (1, 2, 3, 4), if the next term follows the pattern, the next term is 5.
- Reasoning Type: Deductive
- Explanation: The conclusion is derived from the observed pattern (each term increases by 1) and the general rule of arithmetic sequences. This is a logical deduction.

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#### 6. Scientists are developing drugs that target specific cancers. This will lead to cures.
- Reasoning Type: Inductive
- Explanation: The conclusion is based on the progress made in developing targeted drugs (specific instances). The expectation that this will lead to cures is an inductive generalization.

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#### 7. The garbage truck comes once a week after Tuesday, Thursday, and Saturday. It will come this Tuesday.
- Reasoning Type: Deductive
- Explanation: The conclusion is based on the established schedule (general rule: the truck comes after Tuesday, Thursday, and Saturday). This is a logical deduction.

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#### 8. My car tires are inflated (high) and my gas tank is full.
- Reasoning Type: Deductive
- Explanation: The conclusion is based on direct observation (specific instances: tires are inflated, gas tank is full). There is no generalization involved.

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#### 9. The price of gas has gone down every day this week. The price of gas will go down tomorrow.
- Reasoning Type: Inductive
- Explanation: The conclusion is based on the observed trend over the past week (specific instances). The expectation that the trend will continue is an inductive generalization.

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#### 10. Cats Meow Traggle has made better games. You can trust Traggle with your game.
- Reasoning Type: Inductive
- Explanation: The conclusion is based on the past performance of Cats Meow Traggle (specific instances). The trust in future performance is an inductive generalization.

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#### 11. All presidents except one have been male. The next president will be male.
- Reasoning Type: Inductive
- Explanation: The conclusion is based on historical data (specific instances: most presidents have been male). The expectation that the next president will also be male is an inductive generalization.

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#### 12. George Washington was the first President of the United States under the U.S. Constitution. The next was John Adams.
- Reasoning Type: Deductive
- Explanation: The conclusion is based on historical facts (general knowledge: George Washington was the first President, followed by John Adams). This is a logical deduction.

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#### 13. The Astros (a baseball team) lost both games. They will lose their third game.
- Reasoning Type: Inductive
- Explanation: The conclusion is based on the team's recent performance (specific instances: two losses). The expectation that they will lose again is an inductive generalization.

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#### 14. If I wait up, I will oversleep.
- Reasoning Type: Deductive
- Explanation: The conclusion is based on a general rule (if you wait up, you will oversleep) applied to a specific instance (waiting up). This is a logical deduction.

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#### 15. The last time Mark (a close friend) saw me, he called me later that day.
- Reasoning Type: Inductive
- Explanation: The conclusion is based on past behavior (specific instance: Mark called after seeing the person). The expectation that he will do the same again is an inductive generalization.

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Final Answer:

Here is the list with the reasoning type identified for each statement:

1. Inductive
2. Inductive
3. Deductive
4. Deductive
5. Deductive
6. Inductive
7. Deductive
8. Deductive
9. Inductive
10. Inductive
11. Inductive
12. Deductive
13. Inductive
14. Deductive
15. Inductive

Boxed Answer:
\[
\boxed{
\text{Inductive, Inductive, Deductive, Deductive, Deductive, Inductive, Deductive, Deductive, Inductive, Inductive, Inductive, Deductive, Inductive, Deductive, Inductive}
}
\]