Sets online worksheet for Grade 7 - Free Printable

Let's go through each question step by step and solve them with clear explanations.

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Question 1: Match the Term with the Correct Description

We are given a list of terms and descriptions. We need to match each term with its correct definition.

| TERM | DESCRIPTION |
|------|-------------|
| A set | A group of things/objects that have something in common |
| Elements | The objects or things in a set |
| A finite set | A set whose elements CAN be counted |
| An infinite set | A set whose elements CANNOT be counted |
| A null set | A set with no elements |

✔ Correct Matching:

- A set → *A group of things/objects that have something in common*
✔️ This is the definition of a set — a collection of distinct objects.

- Elements → *The objects or things in a set*
✔️ These are the individual items in a set.

- A finite set → *A set whose elements CAN be counted*
✔️ Finite sets have a limited number of elements (e.g., {1,2,3}).

- An infinite set → *A set whose elements CANNOT be counted*
✔️ Infinite sets go on forever (e.g., all natural numbers).

- A null set → *A set with no elements*
✔️ Also called an empty set, denoted as ∅ or {}.

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✔ Final Answer for Question 1:

| TERM | DESCRIPTION |
|------|-------------|
| A set | A group of things/objects that have something in common |
| Elements | The objects or things in a set |
| A finite set | A set whose elements CAN be counted |
| An infinite set | A set whose elements CANNOT be counted |
| A null set | A set with no elements |

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Question 2: Is the set infinite, finite, or null?

Let’s analyze each set:

#### i) {3, 5, 7, ...}
- This is a sequence of odd numbers starting from 3, continuing indefinitely.
- The "..." indicates it goes on forever.
- So, this is an infinite set.

✔ Answer: Infinite

#### ii) {1, 2, 3, 4}
- There are exactly 4 elements.
- Can be counted.
- So, this is a finite set.

✔ Answer: Finite

#### iii) The days of the week beginning with 'c'
- Days of the week: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday.
- None begin with 'c'.
- So, there are no elements.
- This is a null set.

✔ Answer: Null

#### iv) {10, 20, 30, ..., 200}
- This is a sequence of multiples of 10 from 10 to 200.
- It has a start and end point: 10, 20, ..., 200.
- Number of elements: (200 ÷ 10) = 20 elements.
- So, it's finite.

✔ Answer: Finite

#### v) Babies born on the planet Venus
- Venus is not inhabited by humans.
- No babies have been born there.
- So, this set has no elements.
- Therefore, it's a null set.

✔ Answer: Null

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✔ Final Answers for Question 2:

i) Infinite
ii) Finite
iii) Null
iv) Finite
v) Null

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Question 3: Set A and Set B

We are given:

- Set A: Even numbers greater than 1 and less than 15
→ Even numbers: 2, 4, 6, 8, 10, 12, 14
→ So, A = {2, 4, 6, 8, 10, 12, 14}

- Set B: Odd numbers greater than 0 and less than 14
→ Odd numbers: 1, 3, 5, 7, 9, 11, 13
→ So, B = {1, 3, 5, 7, 9, 11, 13}

Now, fill in numbers to make the statements true:

#### i) ____ ∈ A
→ Pick any element from Set A. For example: 6
✔️ Because 6 is in Set A.

#### ii) ____ ∉ A
→ Pick a number not in Set A. For example: 5
✔️ 5 is odd, not in A.

#### iii) ____ ∈ B
→ Pick any element from Set B. For example: 7
✔️ 7 is in B.

#### iv) ____ ∉ B
→ Pick a number not in Set B. For example: 2
✔️ 2 is even, not in B.

> Note: Any valid answer works. These are just examples.

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✔ Final Answers for Question 3:

i) 6 ∈ A
ii) 5 ∉ A
iii) 7 ∈ B
iv) 2 ∉ B

*(Other valid answers include: 4, 8, 10, etc. for i); 1, 3, 9, etc. for ii); 1, 3, 5, etc. for iii); 4, 6, 8, etc. for iv)*

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✔ Summary of All Answers:

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#### Question 1: Matching
| TERM | CORRECT DESCRIPTION |
|------|---------------------|
| A set | A group of things/objects that have something in common |
| Elements | The objects or things in a set |
| A finite set | A set whose elements CAN be counted |
| An infinite set | A set whose elements CANNOT be counted |
| A null set | A set with no elements |

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#### Question 2: Type of Set
i) {3, 5, 7, ...} → Infinite
ii) {1, 2, 3, 4} → Finite
iii) Days of week starting with 'c' → Null
iv) {10, 20, 30, ..., 200} → Finite
v) Babies born on Venus → Null

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#### Question 3: Fill in the blanks
i) 6 ∈ A
ii) 5 ∉ A
iii) 7 ∈ B
iv) 2 ∉ B

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Let me know if you'd like this formatted as a printable answer sheet!