Inductive and Deductive Reasoning | CK-12 Foundation - Free Printable

Let's analyze each situation in the handout to determine whether it is an example of inductive reasoning or deductive reasoning. Then, I'll explain each one clearly.

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🔍 Definitions:

- Inductive Reasoning: Drawing general conclusions from specific observations. It’s based on patterns and probabilities, but not guaranteed.
- Deductive Reasoning: Drawing specific conclusions from general principles or premises. If the premises are true, the conclusion must be true.

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Now, let's go through each box:

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#### 1. Raul, Todd, and Brandon at track meet
> At the first track meet of the year, Raul, Todd and Brandon all tied for 1st place. In the last track meet of the year, Raul finished well ahead of Todd and Brandon. You concluded that Raul trained the hardest.

✔ Inductive Reasoning

➡️ Why? The conclusion ("Raul trained the hardest") is inferred from observed performance improvement. But this isn't logically certain — maybe Raul had better luck, better weather, etc. It’s a *generalization* based on limited evidence.

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#### 2. Mike walking home
> Mike walks home from school and it normally takes him 20 minutes. He walked home faster one day and made it in 15 minutes. The next day he makes it in 12 minutes. Mike makes the conjecture he could make the trip in 8 mins.

✔ Inductive Reasoning

➡️ Why? Mike observes a pattern (decreasing time) and predicts a future outcome (8 minutes). This is a prediction based on trend, not logical necessity.

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#### 3. Number sequence: 1, 1, 2, 3, 5, 8, 13...

✔ Inductive Reasoning

➡️ Why? Recognizing a pattern (Fibonacci sequence) and predicting the next number is inductive. You're observing a pattern and making a generalization about what comes next.

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#### 4. All cookies are made with sugar. Oreo’s are a cookie so Rosa knows Oreo’s are made with sugar.

✔ Deductive Reasoning

➡️ Why?
Premise 1: All cookies are made with sugar.
Premise 2: Oreos are cookies.
Conclusion: Oreos are made with sugar.
This is a classic syllogism — a general rule applied to a specific case → deduction.

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#### 5. 3-D movies every Friday
> For the past three Fridays, a 3-D movie has come out in theaters. Josh concluded that this Friday, a 3-D movie will come out in theaters.

✔ Inductive Reasoning

➡️ Why? Based on repeated observation, Josh predicts the same pattern will continue. But there’s no guarantee — it’s a pattern-based prediction, not a logical certainty.

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#### 6. Snow when temperature is below 32°F
> It snows when the temperature is below 32°F. The temperature is 35°F. Therefore, it is not snowing.

✔ Deductive Reasoning

➡️ Why?
General rule: Below 32°F → snow.
Temperature is 35°F → above threshold.
Therefore, no snow.
This follows logically from the premise — if the condition isn’t met, the result doesn’t happen. Valid deduction.

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#### 7. Diet and weight loss
> You have been on a diet for 3 weeks and lose 3 pounds. You conclude that you can lose 20 more pounds in the next 20 weeks.

✔ Inductive Reasoning

➡️ Why? You’re extrapolating from a small sample (3 weeks) to predict future results. Assumes the rate continues, which isn’t guaranteed — pattern-based generalization.

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#### 8. Lines AB and CD intersect at point P. Therefore, Points A, B, C, and D are non-collinear.

✔ Deductive Reasoning

➡️ Why?
If two lines intersect at a point, they cannot all lie on the same straight line (unless it's the same line). So, the points are not collinear. This is a geometric logical consequence from definitions.

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#### 9. Triangle pattern
> [Image shows triangles arranged in increasing numbers: 1, 2, 3, 4...]

✔ Inductive Reasoning

➡️ Why? You observe a pattern in the figures and infer the next one. Even though it may seem obvious, it's still based on observation and pattern recognition, not logical necessity.

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#### 10. LPS college trip
> LPS takes some Sophomores and Juniors on a Southern California college trip in the spring. I am a Sophomore so I may go on the college trip in the spring.

✔ Inductive Reasoning

➡️ Why? "May go" indicates possibility, not certainty. The student infers from a general policy (some sophomores go) that they might be included. But since it says “some,” not “all,” it’s not guaranteed. So it's probabilistic inference, not deductive.

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#### 11. Frances and laptops
> Frances knows that a Sony laptop costs less than a MacBook laptop. She also knows that all other laptops cost less than a Sony. Frances reasons that a MacBook is the most expensive laptop.

✔ Deductive Reasoning

➡️ Why?
- Sony < MacBook
- All others < Sony
→ Therefore, all others < Sony < MacBook
So MacBook is most expensive.
This is a chain of logical comparisons — deductive.

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#### 12. Vertical angles ∠C ≅ ∠D
> ∠C and ∠D are vertical angles. ∠C ≅ ∠D.

✔ Deductive Reasoning

➡️ Why? From geometry, we know that vertical angles are always congruent. So given the premise that they are vertical angles, the conclusion follows necessarily — deduction.

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✔ Final T-Chart Summary

| Inductive Reasoning | Deductive Reasoning |
|--------------------------|--------------------------|
| 1. Raul trained hardest | 4. Oreos made with sugar |
| 2. Mike walks faster → 8 min | 6. Temperature 35°F → no snow |
| 3. Number sequence (Fibonacci) | 8. Intersecting lines → non-collinear |
| 5. 3-D movies every Friday | 11. MacBook is most expensive |
| 7. Lose 3 lbs in 3 weeks → 20 lbs in 20 weeks | 12. Vertical angles are congruent |
| 9. Triangle pattern | |
| 10. I may go on trip (as sophomore) | |

> Note: #10 is tricky — technically, it’s inductive because “may” implies possibility, not certainty. If it said “I will go,” it would be stronger, but as written, it’s probabilistic.

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🎯 Bonus: Create Your Own Example

Here’s one for each:

#### Inductive:
> Every time I’ve eaten spicy food, I’ve gotten heartburn. So I think spicy food causes my heartburn.

➡️ Pattern-based generalization.

#### Deductive:
> All mammals are warm-blooded. A whale is a mammal. Therefore, a whale is warm-blooded.

➡️ General rule → specific instance.

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Let me know if you'd like this formatted into a printable T-chart!