Let’s go through each item one by one. Remember, a
set is a well-defined collection of distinct objects — meaning everyone should agree on what belongs in it and what doesn’t. If something is vague or depends on opinion (like “tall” or “easy”), then it’s NOT a set.
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(a) Capitals of all countries in Europe.
→ This IS a set. Why? Because there’s a clear list: Paris, Berlin, Rome, etc. Everyone agrees which cities are capitals of European countries.
(b) Numbers divisible by 7
→ This IS a set. Even though there are infinitely many, we can clearly say if a number belongs (like 7, 14, 21…) or not (like 5 or 10). It’s well-defined.
(c) All tall buildings in Shanghai
→ NOT a set. What does “tall” mean? 50 meters? 100 floors? Different people have different ideas. So it’s not well-defined.
(d) All squares which is easy to draw.
→ NOT a set. “Easy to draw” is subjective. One person might find a small square easy; another might think only big ones are easy. Not objective.
(e) First five even numbers
→ IS a set. That’s {2, 4, 6, 8, 10}. Clear and agreed upon.
(f) First five odd numbers
→ IS a set. That’s {1, 3, 5, 7, 9}. Also clear.
(g) All 6 sided figures
→ IS a set. These are hexagons. Whether regular or irregular, if it has 6 sides, it’s included. Well-defined.
(h) First 6 days of a month.
→ IS a set. Days 1, 2, 3, 4, 5, 6. Always the same. No confusion.
(i) All girls who are shorter than 4 ft.
→ IS a set. We can measure height. If someone is under 4 feet, they’re in. Over? Out. Objective.
(j) All cars in the parking lot
→ IS a set. At any given time, you can count them. They’re physically there. Well-defined for that moment.
(k) All smart phones in a mobile phone showroom
→ IS a set. Again, at a specific time, you can list them. Maybe iPhone, Samsung, etc. — but as long as they’re in the showroom, it’s defined.
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Final Answer:
(a) Yes – well-defined
(b) Yes – well-defined
(c) No – “tall” is not well-defined
(d) No – “easy to draw” is subjective
(e) Yes – {2, 4, 6, 8, 10}
(f) Yes – {1, 3, 5, 7, 9}
(g) Yes – all hexagons
(h) Yes – days 1 to 6
(i) Yes – measurable height
(j) Yes – actual cars present
(k) Yes – phones currently in showroom
Parent Tip: Review the logic above to help your child master the concept of set worksheet.
