Worksheet on identifying inductive and deductive reasoning with examples for analysis.

Let's analyze each of the seven arguments one by one, identifying whether they use inductive or deductive reasoning, and then evaluate their strength or soundness accordingly.

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

- Type of Reasoning: Inductive
- Strength: Strong
- Explanation: This argument is based on past observations (winning 3 times) to predict a future outcome (likely winning again). It does not guarantee the conclusion but makes a probable prediction based on patterns. Since the evidence is consistent and repeated, it’s a strong inductive argument.

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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.

- Type of Reasoning: Deductive
- Soundness: Unsound
- Why?: The argument has a valid form (disjunctive syllogism), but the first premise is false. It assumes only two possibilities: best or worst. But there are likely many other possible rankings (e.g., middle of the class). So, the premise "Either you are the best or the worst" is false, making the argument unsound even though it's logically valid.

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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.

- Type of Reasoning: Inductive
- Strength: Strong
- Explanation: This uses statistical data (70% Democrats) to make a probable prediction about election results. While it doesn’t guarantee victory (due to voter turnout, independent voters, etc.), the conclusion is highly plausible given the data. Thus, it’s a strong inductive argument.

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

- Type of Reasoning: Deductive
- Soundness: Sound
- Explanation: The argument follows a classic deductive structure:
- All A are B.
- C is an A.
- Therefore, C is B.
- Premises are accepted as true (platypuses are mammals; mammals are warm-blooded).
- Conclusion necessarily follows.
- So, it’s both valid and sound.

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

- Type of Reasoning: Deductive
- Soundness: Unsound
- Why?: The first premise ("If it is April, it is warm outside") is false — April can be cold in many places. The argument is valid in form (modus ponens), but since the premise is not universally true, the argument is unsound. The conclusion doesn't necessarily follow from a false premise.

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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.

- Type of Reasoning: Inductive
- Strength: Weak
- Explanation: This is a classic example of post hoc fallacy (assuming causation from correlation). Just because two events occurred together doesn't mean one caused the other. The reasoning is inductive but extremely weak because it ignores alternative explanations (weather patterns, etc.) and draws a causal conclusion from mere coincidence.

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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...

- Note: The sentence is cut off, but we can still analyze what’s given.
- Type of Reasoning: Inductive
- Strength: Strong
- Explanation: Multiple reliable sources (professional polling firms) report a consistent result (70% approval). This is a strong inductive argument based on converging evidence. The conclusion (that most New Yorkers approve) is highly probable, though not certain. Since the data comes from reputable sources and is consistent, it’s a strong inductive inference.

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✔ Summary Table:

| # | Reasoning Type | Strength / Soundness | Notes |
|---|----------------|------------------------|-------|
| 1 | Inductive | Strong | Based on repeated experience |
| 2 | Deductive | Unsound | Valid form, but false premise (not only best/worst) |
| 3 | Inductive | Strong | Probable conclusion from statistical data |
| 4 | Deductive | Sound | Valid and all premises true |
| 5 | Deductive | Unsound | Valid form, but false premise (April ≠ always warm) |
| 6 | Inductive | Weak | False causation from correlation |
| 7 | Inductive | Strong | Consistent data from multiple reliable sources |

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