Students practice identifying objective versus subjective sets in this 'Going to the Supermarket' themed math exercise.
Grade 7 math worksheet classifying well-defined and not well-defined sets with a supermarket illustration.
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Show Answer Key & Explanations
Step-by-step solution for: Set and Set Notation Themed Math Worksheets | Aged 11-13
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Show Answer Key & Explanations
Step-by-step solution for: Set and Set Notation Themed Math Worksheets | Aged 11-13
Here's the classification of each set as well-defined or not well-defined, along with a clear explanation for each:
---
1. set of tall buildings in your place
→ not well-defined
*Explanation:* “Tall” is subjective — what one person considers tall, another might not. There’s no universal or objective height threshold given, so we can’t definitively say which buildings belong to this set.
---
2. set of electronic devices
→ well-defined
*Explanation:* An electronic device is an object that operates using electricity and circuits (e.g., phone, laptop, TV). This is a technical category with generally accepted criteria, so membership is objectively determinable.
---
3. set of bakeshops
→ well-defined
*Explanation:* A bakeshop is a business that primarily sells baked goods (bread, cakes, pastries). While some shops may sell other items too, the core function defines it. You can objectively identify whether a shop fits this description.
---
4. set of delicious foods
→ not well-defined
*Explanation:* “Delicious” is based on personal taste — one person’s favorite food might be another’s least favorite. No objective standard exists, so this set cannot be clearly defined.
---
5. set of best coffee shops
→ not well-defined
*Explanation:* “Best” is subjective and depends on criteria like taste, ambiance, price, etc. Without specifying what “best” means, we can’t objectively determine which coffee shops belong to this set.
---
6. set of plants
→ well-defined
*Explanation:* In biology, a plant is a living organism belonging to the kingdom Plantae — typically photosynthetic, rooted, and multicellular. This is a scientific classification with clear boundaries.
---
7. set of car brands
→ well-defined
*Explanation:* Car brands are officially registered trademarks (e.g., Toyota, Ford, BMW). There’s a finite, publicly known list, and you can objectively verify if a name is a recognized car brand.
---
8. set of attractive colors
→ not well-defined
*Explanation:* “Attractive” is entirely subjective — color preference varies by culture, personal taste, and context. No objective measure exists to define which colors are “attractive.”
---
9. set of schools
→ well-defined
*Explanation:* A school is an institution dedicated to education, usually with formal structure, teachers, students, and curriculum. While definitions vary slightly by country, the general concept is clear and verifiable.
---
10. set of beautiful girls
→ not well-defined
*Explanation:* “Beautiful” is a highly subjective term influenced by cultural norms, personal opinion, and bias. There is no objective standard to determine who belongs to this set.
---
1. not well-defined
2. well-defined
3. well-defined
4. not well-defined
5. not well-defined
6. well-defined
7. well-defined
8. not well-defined
9. well-defined
10. not well-defined
---
📌 Key Concept Recap:
A set is well-defined if you can objectively determine whether any given object belongs to it or not — there should be no ambiguity or personal opinion involved. If the definition relies on feelings, opinions, or vague terms (like “best,” “beautiful,” “delicious”), it’s not well-defined.
---
1. set of tall buildings in your place
→ not well-defined
*Explanation:* “Tall” is subjective — what one person considers tall, another might not. There’s no universal or objective height threshold given, so we can’t definitively say which buildings belong to this set.
---
2. set of electronic devices
→ well-defined
*Explanation:* An electronic device is an object that operates using electricity and circuits (e.g., phone, laptop, TV). This is a technical category with generally accepted criteria, so membership is objectively determinable.
---
3. set of bakeshops
→ well-defined
*Explanation:* A bakeshop is a business that primarily sells baked goods (bread, cakes, pastries). While some shops may sell other items too, the core function defines it. You can objectively identify whether a shop fits this description.
---
4. set of delicious foods
→ not well-defined
*Explanation:* “Delicious” is based on personal taste — one person’s favorite food might be another’s least favorite. No objective standard exists, so this set cannot be clearly defined.
---
5. set of best coffee shops
→ not well-defined
*Explanation:* “Best” is subjective and depends on criteria like taste, ambiance, price, etc. Without specifying what “best” means, we can’t objectively determine which coffee shops belong to this set.
---
6. set of plants
→ well-defined
*Explanation:* In biology, a plant is a living organism belonging to the kingdom Plantae — typically photosynthetic, rooted, and multicellular. This is a scientific classification with clear boundaries.
---
7. set of car brands
→ well-defined
*Explanation:* Car brands are officially registered trademarks (e.g., Toyota, Ford, BMW). There’s a finite, publicly known list, and you can objectively verify if a name is a recognized car brand.
---
8. set of attractive colors
→ not well-defined
*Explanation:* “Attractive” is entirely subjective — color preference varies by culture, personal taste, and context. No objective measure exists to define which colors are “attractive.”
---
9. set of schools
→ well-defined
*Explanation:* A school is an institution dedicated to education, usually with formal structure, teachers, students, and curriculum. While definitions vary slightly by country, the general concept is clear and verifiable.
---
10. set of beautiful girls
→ not well-defined
*Explanation:* “Beautiful” is a highly subjective term influenced by cultural norms, personal opinion, and bias. There is no objective standard to determine who belongs to this set.
---
✔ Final Answers:
1. not well-defined
2. well-defined
3. well-defined
4. not well-defined
5. not well-defined
6. well-defined
7. well-defined
8. not well-defined
9. well-defined
10. not well-defined
---
📌 Key Concept Recap:
A set is well-defined if you can objectively determine whether any given object belongs to it or not — there should be no ambiguity or personal opinion involved. If the definition relies on feelings, opinions, or vague terms (like “best,” “beautiful,” “delicious”), it’s not well-defined.
Parent Tip: Review the logic above to help your child master the concept of set notation worksheet.
