Worksheet on inductive and deductive reasoning with examples for analysis.

Let's analyze each argument step by step to determine whether it uses inductive or deductive reasoning, and then evaluate its strength or validity accordingly.

---

1. I have beaten Tommy the least three times we played chess. We are playing again today. I will probably win again.

- Reasoning Type: Inductive
- This argument generalizes from past experiences (beating Tommy in previous games) to predict future outcomes (winning again today). It does not guarantee the conclusion but suggests a high likelihood based on past data.

- Strength: Weak
- The argument is weak because it relies on a small sample size (only three games) to make a prediction. Past performance does not necessarily indicate future results, especially with such limited data.

---

2. Either you are the best student in the class, or you are the worst student in the class. You are not the worst student in the class. Therefore, you are the best student in the class.

- Reasoning Type: Deductive
- This argument follows a logical structure: If A or B is true, and B is false, then A must be true. It is a form of disjunctive syllogism.

- Soundness: Sound
- The argument is valid because the logic is correct: if the premises are true, the conclusion must follow. There are no false premises here, so the argument is sound.

---

3. Seventy percent of registered voters in Clarksville are Democrats. Most likely, the Democratic candidate will get a majority of votes in Clarksville in the next election.

- Reasoning Type: Inductive
- This argument generalizes from statistical data (70% of voters being Democrats) to predict the outcome of an election. It does not guarantee the conclusion but suggests a high probability based on the given data.

- Strength: Strong
- The argument is strong because it is based on a significant statistical trend (70% of voters being Democrats). While it does not account for other factors like voter turnout or preferences, the high percentage provides a reasonable basis for the prediction.

---

4. All mammals are warm-blooded. A platypus is a mammal. Therefore, a platypus is warm-blooded.

- Reasoning Type: Deductive
- This argument follows a logical structure: If all members of a category (mammals) have a certain property (warm-blooded), and a specific member (platypus) belongs to that category, then the specific member must also have that property.

- Soundness: Sound
- The argument is valid because the logic is correct: if the premises are true, the conclusion must follow. Both premises ("All mammals are warm-blooded" and "A platypus is a mammal") are true, so the argument is sound.

---

5. If it is April, it is warm outside. Today is April 27. Therefore, it is warm outside.

- Reasoning Type: Deductive
- This argument follows a conditional statement: If P (it is April), then Q (it is warm outside). Given that P is true (today is April 27), the argument concludes that Q must be true.

- Soundness: Unsound
- The argument is invalid because the premise "If it is April, it is warm outside" is not universally true. Weather can vary significantly depending on location and other factors, so the conclusion does not necessarily follow from the premises.

---

6. On Sunday, Wednesday, and Thursday last week I wore my blue shoes, and each of those days it rained. Clearly, my blue shoes are the cause of the rain.

- Reasoning Type: Inductive
- This argument attempts to establish a causal relationship (blue shoes causing rain) based on observed correlations (wearing blue shoes on rainy days).

- Strength: Weak
- The argument is weak because correlation does not imply causation. Wearing blue shoes on rainy days does not mean the shoes caused the rain. Other factors, such as weather patterns, are more likely explanations.

---

7. Five different surveys by professional polling firms found that 70 percent of New York residents believe the governor is doing a good job during the

- Reasoning Type: Inductive
- This argument generalizes from survey data (70% of respondents believing the governor is doing a good job) to conclude something about the broader population of New York residents.

- Strength: Strong
- The argument is strong because it is based on multiple independent surveys conducted by professional polling firms. The consistency across surveys and the use of professional methods suggest that the conclusion is reliable. However, it still relies on sampling and may not capture every individual's opinion perfectly.

---

Final Answers:

1. Inductive, Weak
- Explanation: Based on limited past data (three games), the conclusion is not strongly supported.

2. Deductive, Sound
- Explanation: The logical structure is valid, and the premises are true.

3. Inductive, Strong
- Explanation: The high percentage of Democrats provides a strong basis for predicting the election outcome.

4. Deductive, Sound
- Explanation: The logical structure is valid, and both premises are true.

5. Deductive, Unsound
- Explanation: The premise "If it is April, it is warm outside" is not universally true, making the argument invalid.

6. Inductive, Weak
- Explanation: Correlation does not imply causation; the conclusion is not strongly supported.

7. Inductive, Strong
- Explanation: Multiple independent surveys provide a strong basis for the conclusion.

---

Boxed Final Answer:

\[
\boxed{
\begin{array}{ll}
1. & \text{Inductive, Weak} \\
2. & \text{Deductive, Sound} \\
3. & \text{Inductive, Strong} \\
4. & \text{Deductive, Sound} \\
5. & \text{Deductive, Unsound} \\
6. & \text{Inductive, Weak} \\
7. & \text{Inductive, Strong} \\
\end{array}
}
\]