Worksheet on Intro to Reasoning: Inductive and Deductive Reasoning with Examples and Practice Scenarios.

Let's solve and explain the worksheet step by step.

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Part 1: Fill in the Blanks

#### Reasoning – A systematic way of coming to a conclusion.

> ✔ Answer: *Conclusion*

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#### 1. Inductive Reasoning
- Coming to a conclusion based on observations or patterns. It starts with specific examples and goes to a general conclusion.

> ✔ Fill-ins:
> - observations
> - patterns
> - specific examples
> - general conclusion

> 🔍 Explanation: Inductive reasoning moves from specific instances to broader generalizations. For example, seeing rain two days in a row leads to the prediction that it will rain again — this is not guaranteed but based on observed trends.

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#### 2. Deductive Reasoning
- Coming to a conclusion based on general principles. It starts with general premises and goes to a specific conclusion.

> ✔ Fill-ins:
> - general principles
> - general premises
> - specific conclusion

> 🔍 Explanation: Deductive reasoning uses established rules or facts to reach a logical, certain conclusion. If all humans need water and Sarah is human, then she must need water — this follows logically from general truths.

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Part 2: Identify Type of Reasoning (I = Inductive, D = Deductive)

Now let’s analyze each scenario:

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#### 1. Joe flipped a quarter and it landed on tails 3 times. Therefore, it will land on tails when he flips it again.

> ✔ Answer: I (Inductive)
> 🔍 Why? This is based on repeated observations (three tails) leading to a prediction about the future. It does not use general laws or logic — just pattern recognition. Even though it's flawed (coins are random), it's still inductive because it generalizes from past events.

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#### 2. Apples are a type of fruit. Granny Smith is a type of apple, so it is a fruit.

> ✔ Answer: D (Deductive)
> 🔍 Why? This follows a logical structure:
> - All apples → fruit (general principle)
> - Granny Smith → apple (specific case)
> - Therefore, Granny Smith → fruit (specific conclusion)
>
> This is deductive: starting with general categories and applying them to a specific instance.

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#### 3. Acute angles are less than 90°. An angle is 47° so it is an acute angle.

> ✔ Answer: D (Deductive)
> 🔍 Why? The definition of acute angles is given (general rule), and we apply it to a specific angle (47°). Since 47° < 90°, it fits the definition. This is logical deduction, not based on observation.

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#### 4. Julie is from Sweden and has blonde hair. Therefore, all people from Sweden have blonde hair.

> ✔ Answer: I (Inductive)
> 🔍 Why? This draws a general conclusion (all Swedes have blonde hair) from one specific example (Julie). Even though it's incorrect, the reasoning process is inductive — going from a single observation to a broad generalization.

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✔ Final Answers:

| Example | Reasoning Type |
|--------|----------------|
| 1 | I (Inductive) |
| 2 | D (Deductive) |
| 3 | D (Deductive) |
| 4 | I (Inductive) |

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📌 Summary of Key Concepts:

- Inductive Reasoning: Specific → General (based on patterns/observations). May be uncertain.
- Deductive Reasoning: General → Specific (based on logic/rules). If premises are true, conclusion is valid.

This worksheet helps distinguish between these two fundamental types of reasoning used in math, science, and everyday thinking!