Inductive and Deductive Reasoning | CK-12 Foundation - Free Printable
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Step-by-step solution for: Inductive and Deductive Reasoning | CK-12 Foundation
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Show Answer Key & Explanations
Step-by-step solution for: Inductive and Deductive Reasoning | CK-12 Foundation
Let’s go through each situation one by one and decide if it’s inductive or deductive reasoning.
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🔹 Inductive Reasoning: You look at specific examples or patterns and make a general conclusion. It’s like guessing the rule based on what you’ve seen so far. The conclusion is likely, but not guaranteed to be true.
🔹 Deductive Reasoning: You start with a general rule or fact, and apply it to a specific case to reach a certain conclusion. If the starting facts are true, the conclusion MUST be true.
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Now let’s analyze each box:
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Box 1 (Top Left)
> 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.
→ This is inductive. You’re looking at two events and making a guess about why Raul improved — you didn’t observe his training, you inferred it from results.
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Box 2 (Top Right)
> 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.
→ This is inductive. He’s seeing a pattern (20 → 15 → 12) and guessing the next step (8). But there’s no guarantee it will keep going down that fast.
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Box 3 (Second Row Left)
> 1, 1, 2, 3, 5, 8, 13...
→ This is the Fibonacci sequence. If someone says “the next number is 21” because each number is the sum of the two before, that’s inductive — they’re spotting a pattern and predicting the next term.
*(Note: The image doesn’t state a conclusion, but since it’s presented as a reasoning task, we assume the implied reasoning is “next number is 21” based on pattern.)*
→ Inductive
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Box 4 (Second Row Right)
> All cookies are made with sugar. Oreo’s are a cookie so Rosa knows Oreo’s are made with sugar.
→ This is deductive. Starts with a general rule (“all cookies have sugar”), applies it to a specific case (“Oreos are cookies”), and concludes something that must be true if the premises are true.
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Box 5 (Third Row Left)
> 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. He’s seeing a pattern over 3 weeks and assuming it continues. But it might not — maybe next Friday is different.
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Box 6 (Third Row Right)
> It snows when the temperature is below 32° F. The temperature is 35° F. Therefore, it is not snowing.
→ Deductive. General rule: snow only if temp < 32°. Specific fact: temp = 35°. Conclusion: no snow. Logically follows.
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Box 7 (Fourth Row Left)
> 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. Assuming the rate will stay the same (1 lb/week), but bodies don’t always work that way. It’s a prediction based on past data.
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Box 8 (Fourth Row Right)
> AB and CD intersect at point P. Therefore, Points A, B, C, and D are non-collinear.
→ Deductive. If two lines intersect at a point, and each line has two distinct points, then unless all four lie on the same line (which they can’t if two lines cross at one point), they must be non-collinear. This uses geometry rules to conclude something certain.
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Box 9 (Fifth Row Left)
> Frances knows that a Sony laptop cost less than a MacBook laptop. She also knows that all other laptops costs less than a Sony. Frances reasons that a MacBook is the most expensive laptop.
→ Deductive.
Premise 1: Sony < MacBook
Premise 2: All others < Sony
Therefore: All others < Sony < MacBook → MacBook is most expensive.
Logical chain — must be true if premises are true.
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Box 10 (Fifth Row Right)
> 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. The statement says “some” Sophomores go — not all. So being a Sophomore doesn’t guarantee you’ll go. The conclusion (“I may go”) is probabilistic, not certain.
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Box 11 (Bottom Right)
> ∠C and ∠D are vertical angles. ∠C ≅ ∠D.
→ Deductive. Vertical angles are always congruent — that’s a geometric theorem. So if they’re vertical angles, they must be congruent. No guessing — it’s a rule.
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✔ Final Classification:
1. Inductive
2. Inductive
3. Inductive
4. Deductive
5. Inductive
6. Deductive
7. Inductive
8. Deductive
9. Deductive
10. Inductive
11. Deductive
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Final Answer:
Inductive, Inductive, Inductive, Deductive, Inductive, Deductive, Inductive, Deductive, Deductive, Inductive, Deductive
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🔹 Inductive Reasoning: You look at specific examples or patterns and make a general conclusion. It’s like guessing the rule based on what you’ve seen so far. The conclusion is likely, but not guaranteed to be true.
🔹 Deductive Reasoning: You start with a general rule or fact, and apply it to a specific case to reach a certain conclusion. If the starting facts are true, the conclusion MUST be true.
---
Now let’s analyze each box:
---
Box 1 (Top Left)
> 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.
→ This is inductive. You’re looking at two events and making a guess about why Raul improved — you didn’t observe his training, you inferred it from results.
---
Box 2 (Top Right)
> 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.
→ This is inductive. He’s seeing a pattern (20 → 15 → 12) and guessing the next step (8). But there’s no guarantee it will keep going down that fast.
---
Box 3 (Second Row Left)
> 1, 1, 2, 3, 5, 8, 13...
→ This is the Fibonacci sequence. If someone says “the next number is 21” because each number is the sum of the two before, that’s inductive — they’re spotting a pattern and predicting the next term.
*(Note: The image doesn’t state a conclusion, but since it’s presented as a reasoning task, we assume the implied reasoning is “next number is 21” based on pattern.)*
→ Inductive
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Box 4 (Second Row Right)
> All cookies are made with sugar. Oreo’s are a cookie so Rosa knows Oreo’s are made with sugar.
→ This is deductive. Starts with a general rule (“all cookies have sugar”), applies it to a specific case (“Oreos are cookies”), and concludes something that must be true if the premises are true.
---
Box 5 (Third Row Left)
> 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. He’s seeing a pattern over 3 weeks and assuming it continues. But it might not — maybe next Friday is different.
---
Box 6 (Third Row Right)
> It snows when the temperature is below 32° F. The temperature is 35° F. Therefore, it is not snowing.
→ Deductive. General rule: snow only if temp < 32°. Specific fact: temp = 35°. Conclusion: no snow. Logically follows.
---
Box 7 (Fourth Row Left)
> 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. Assuming the rate will stay the same (1 lb/week), but bodies don’t always work that way. It’s a prediction based on past data.
---
Box 8 (Fourth Row Right)
> AB and CD intersect at point P. Therefore, Points A, B, C, and D are non-collinear.
→ Deductive. If two lines intersect at a point, and each line has two distinct points, then unless all four lie on the same line (which they can’t if two lines cross at one point), they must be non-collinear. This uses geometry rules to conclude something certain.
---
Box 9 (Fifth Row Left)
> Frances knows that a Sony laptop cost less than a MacBook laptop. She also knows that all other laptops costs less than a Sony. Frances reasons that a MacBook is the most expensive laptop.
→ Deductive.
Premise 1: Sony < MacBook
Premise 2: All others < Sony
Therefore: All others < Sony < MacBook → MacBook is most expensive.
Logical chain — must be true if premises are true.
---
Box 10 (Fifth Row Right)
> 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. The statement says “some” Sophomores go — not all. So being a Sophomore doesn’t guarantee you’ll go. The conclusion (“I may go”) is probabilistic, not certain.
---
Box 11 (Bottom Right)
> ∠C and ∠D are vertical angles. ∠C ≅ ∠D.
→ Deductive. Vertical angles are always congruent — that’s a geometric theorem. So if they’re vertical angles, they must be congruent. No guessing — it’s a rule.
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✔ Final Classification:
1. Inductive
2. Inductive
3. Inductive
4. Deductive
5. Inductive
6. Deductive
7. Inductive
8. Deductive
9. Deductive
10. Inductive
11. Deductive
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Final Answer:
Inductive, Inductive, Inductive, Deductive, Inductive, Deductive, Inductive, Deductive, Deductive, Inductive, Deductive
Parent Tip: Review the logic above to help your child master the concept of inductive reasoning worksheet.
