Elements of Sets Worksheets | Grade1to6.com - Free Printable
Educational worksheet: Elements of Sets Worksheets | Grade1to6.com. Download and print for classroom or home learning activities.
JPG
1239×1754
450.3 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #978844
⭐
Show Answer Key & Explanations
Step-by-step solution for: Elements of Sets Worksheets | Grade1to6.com
▼
Show Answer Key & Explanations
Step-by-step solution for: Elements of Sets Worksheets | Grade1to6.com
This worksheet asks you to determine whether each given description defines a set or not a set, and if not, to explain why.
---
In mathematics, a set is a well-defined collection of distinct objects. “Well-defined” means that for any object, it must be clear and unambiguous whether it belongs to the set or not.
If the description is vague, subjective, or depends on opinion or context, then it does not form a set.
---
Let’s go through each item:
---
Answer: YES — It forms a set.
✔ Reason: The countries in Europe are clearly defined (by international consensus), and each has one official capital city. So, the collection is well-defined.
---
Answer: YES — It forms a set.
✔ Reason: Any integer can be checked mathematically to see if it’s divisible by 7. Even though the set is infinite, it is still well-defined.
---
Answer: NO — Not a set.
✘ Reason: “Tall” is subjective. There’s no universal definition of how tall a building must be to be called “tall.” One person might say 100 meters, another 200 meters. So, it’s not well-defined.
---
Answer: NO — Not a set.
✘ Reason: “Easy to draw” is subjective. What’s easy for one person may be hard for another. No objective criterion exists.
---
Answer: YES — It forms a set.
✔ Reason: The first five even numbers are clearly 2, 4, 6, 8, 10. This is finite and well-defined.
*(Note: Sometimes people debate whether 0 is included, but conventionally in elementary math, “first five even numbers” starts from 2 unless specified otherwise.)*
---
Answer: YES — It forms a set.
✔ Reason: The first five odd numbers are 1, 3, 5, 7, 9. Clearly defined.
---
Answer: YES — It forms a set.
✔ Reason: A 6-sided figure is a hexagon (or any polygon with exactly 6 sides). Although there are many types (regular, irregular, concave, convex), the defining property — having exactly 6 sides — is objective and mathematical.
*(Note: In some contexts, “figure” might be ambiguous, but in math worksheets at this level, it refers to polygons.)*
---
Answer: YES — It forms a set.
✔ Reason: Every month has numbered days. The first six days are always 1st, 2nd, 3rd, 4th, 5th, 6th. Well-defined.
---
Answer: NO — Not a set.
✘ Reason: While height is measurable, the group “all girls” is not well-defined without specifying a context (e.g., “in this school,” “in this country”). Without boundaries, it’s too vague. Also, “girls” could mean children or young women — age is not specified.
> ⚠️ *Note: If the question said “all girls in Grade 6 of ABC School who are shorter than 4 ft,” then it would be a set. But as written, it’s too broad and undefined.*
---
Answer: YES — It forms a set.
✔ Reason: Assuming we’re referring to a specific parking lot (even if not named, in context it’s implied to be a real, physical location), the cars present at a given time are countable and identifiable. So, it’s a well-defined collection.
*(Note: If it were “all cars ever parked anywhere,” that would not be a set — but here, “the parking lot” implies a specific place.)*
---
Answer: YES — It forms a set.
✔ Reason: A specific showroom has a finite, countable number of smartphones on display or for sale. At any moment, you can list them. So, it’s a well-defined set.
---
## ✍️ Final Answers Summary:
| Item | Forms a Set? | Reason (if not) |
|------|--------------|------------------|
| a | ✔ Yes | — |
| b | ✔ Yes | — |
| c | ✘ No | “Tall” is subjective |
| d | ✘ No | “Easy to draw” is subjective |
| e | ✔ Yes | — |
| f | ✔ Yes | — |
| g | ✔ Yes | — |
| h | ✔ Yes | — |
| i | ✘ No | “All girls” is not well-defined; no context |
| j | ✔ Yes | — |
| k | ✔ Yes | — |
---
✔ You can now fill in your worksheet accordingly!
Let me know if you’d like to print or format this as a completed answer sheet!
---
🔑 Key Concept: What is a Set?
In mathematics, a set is a well-defined collection of distinct objects. “Well-defined” means that for any object, it must be clear and unambiguous whether it belongs to the set or not.
If the description is vague, subjective, or depends on opinion or context, then it does not form a set.
---
Let’s go through each item:
---
✔ (a) Capitals of all countries in Europe.
Answer: YES — It forms a set.
✔ Reason: The countries in Europe are clearly defined (by international consensus), and each has one official capital city. So, the collection is well-defined.
---
✔ (b) Numbers divisible by 7
Answer: YES — It forms a set.
✔ Reason: Any integer can be checked mathematically to see if it’s divisible by 7. Even though the set is infinite, it is still well-defined.
---
✘ (c) All tall buildings in Shanghai
Answer: NO — Not a set.
✘ Reason: “Tall” is subjective. There’s no universal definition of how tall a building must be to be called “tall.” One person might say 100 meters, another 200 meters. So, it’s not well-defined.
---
✘ (d) All squares which is easy to draw.
Answer: NO — Not a set.
✘ Reason: “Easy to draw” is subjective. What’s easy for one person may be hard for another. No objective criterion exists.
---
✔ (e) First five even numbers
Answer: YES — It forms a set.
✔ Reason: The first five even numbers are clearly 2, 4, 6, 8, 10. This is finite and well-defined.
*(Note: Sometimes people debate whether 0 is included, but conventionally in elementary math, “first five even numbers” starts from 2 unless specified otherwise.)*
---
✔ (f) First five odd numbers
Answer: YES — It forms a set.
✔ Reason: The first five odd numbers are 1, 3, 5, 7, 9. Clearly defined.
---
✔ (g) All 6 sided figures
Answer: YES — It forms a set.
✔ Reason: A 6-sided figure is a hexagon (or any polygon with exactly 6 sides). Although there are many types (regular, irregular, concave, convex), the defining property — having exactly 6 sides — is objective and mathematical.
*(Note: In some contexts, “figure” might be ambiguous, but in math worksheets at this level, it refers to polygons.)*
---
✔ (h) First 6 days of a month.
Answer: YES — It forms a set.
✔ Reason: Every month has numbered days. The first six days are always 1st, 2nd, 3rd, 4th, 5th, 6th. Well-defined.
---
✘ (i) All girls who are shorter than 4 ft.
Answer: NO — Not a set.
✘ Reason: While height is measurable, the group “all girls” is not well-defined without specifying a context (e.g., “in this school,” “in this country”). Without boundaries, it’s too vague. Also, “girls” could mean children or young women — age is not specified.
> ⚠️ *Note: If the question said “all girls in Grade 6 of ABC School who are shorter than 4 ft,” then it would be a set. But as written, it’s too broad and undefined.*
---
✔ (j) All cars in the parking lot
Answer: YES — It forms a set.
✔ Reason: Assuming we’re referring to a specific parking lot (even if not named, in context it’s implied to be a real, physical location), the cars present at a given time are countable and identifiable. So, it’s a well-defined collection.
*(Note: If it were “all cars ever parked anywhere,” that would not be a set — but here, “the parking lot” implies a specific place.)*
---
✔ (k) All smart phones in a mobile phone showroom
Answer: YES — It forms a set.
✔ Reason: A specific showroom has a finite, countable number of smartphones on display or for sale. At any moment, you can list them. So, it’s a well-defined set.
---
## ✍️ Final Answers Summary:
| Item | Forms a Set? | Reason (if not) |
|------|--------------|------------------|
| a | ✔ Yes | — |
| b | ✔ Yes | — |
| c | ✘ No | “Tall” is subjective |
| d | ✘ No | “Easy to draw” is subjective |
| e | ✔ Yes | — |
| f | ✔ Yes | — |
| g | ✔ Yes | — |
| h | ✔ Yes | — |
| i | ✘ No | “All girls” is not well-defined; no context |
| j | ✔ Yes | — |
| k | ✔ Yes | — |
---
✔ You can now fill in your worksheet accordingly!
Let me know if you’d like to print or format this as a completed answer sheet!
Parent Tip: Review the logic above to help your child master the concept of sets worksheet.
