Class VII Set Theory Practice Worksheet with questions on identifying sets and set notation.

Let's solve the Practice Worksheet on Set Theory step by step, with explanations.

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Question 1: Which of the following are sets? Justify your answer.

A set is a well-defined collection of distinct objects. For something to be a set, its elements must be clearly defined and identifiable (i.e., we should be able to determine whether an object belongs to the collection or not).

Let’s analyze each:

(a) The collection of all the days in a week beginning with the letter 'T'.

- Days starting with 'T': Tuesday, Thursday.
- This is a well-defined collection.
✔ Yes, it is a set.

(b) The collection of all difficult questions in the chapter on sets.

- "Difficult" is subjective — what one person finds difficult, another might not.
- Not well-defined.
✘ Not a set.

(c) The collection of girls in your class.

- Assuming we know who is in the class, this collection is clear and definite.
✔ Yes, it is a set.

(d) The collection of all rivers in India.

- Although large, the rivers in India can be identified and listed.
- Well-defined.
✔ Yes, it is a set.

(e) The collection of all active teachers in the school.

- "Active" may be ambiguous — does it mean currently teaching, employed, or working full-time?
- Could be interpreted differently.
- However, if we assume "active" means currently employed teachers, then it's well-defined.
✔ Yes, it is a set, assuming a clear definition of "active".

(f) The collection of all integers more than -3.

- Integers greater than -3: -2, -1, 0, 1, 2, ...
- This is clearly defined.
✔ Yes, it is a set.

(g) The collection of all beautiful flowers in the park.

- "Beautiful" is subjective.
- Not well-defined.
✘ Not a set.

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✔ Answers for Question 1:

| Item | Is it a set? | Justification |
|------|--------------|-------------|
| (a) | Yes | Clearly defined: Tuesday, Thursday |
| (b) | No | "Difficult" is subjective |
| (c) | Yes | Specific group: girls in class |
| (d) | Yes | Rivers in India are identifiable |
| (e) | Yes | If "active" is clearly defined |
| (f) | Yes | All integers > -3 are well-defined |
| (g) | No | "Beautiful" is subjective |

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Question 2:

Given sets:

- A = {3, 5, 7, 9}
- B = {2, 4, 6, 8, 10}
- C = {12, 14, 18, 20, 24}
- D = {21, 26, 31, 36}

#### (a) State whether true or false:

We check membership (element ∈ or ∉):

(i) 13 ∈ C
C = {12, 14, 18, 20, 24} → 13 is not in C
✘ False

(ii) 4 ∈ A
A = {3, 5, 7, 9} → 4 is not in A
✘ False

(iii) 9 ∈ A
A contains 9 → yes
✔ True

(iv) 24 ∈ C
C contains 24 → yes
✔ True

(v) 5 ∈ D
D = {21, 26, 31, 36} → 5 not in D
✘ False

(vi) 36 ∈ D
D contains 36 → yes
✔ True

(vii) 20 ∈ C
C contains 20 → yes
✔ True

(viii) 9 ∈ A
Already checked → yes
✔ True

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#### (b) Fill in the blanks:

We need to use ∈ (belongs to), ∉ (does not belong to), ⊆ (subset), ⊈ (not subset), etc.

(i) 3 ∈ ___
3 is in A → so: 3 ∈ A

(ii) 4 ___ B
4 is in B → so: 4 ∈ B

(iii) 26 ___ C
26 is not in C → so: 26 ∉ C

(iv) B ___ ___
We need to find which set B is a subset of, or relationship.

But let's look at the options:
B = {2, 4, 6, 8, 10}
C = {12, 14, 18, 20, 24} → no overlap
D = {21, 26, 31, 36} → no overlap
A = {3,5,7,9} → no overlap

So B is not a subset of any of the others.

But perhaps the question is asking: Is B a subset of any other set?

No. But maybe it's asking about element?

Wait — likely typo or formatting issue.

Looking again: (iv) B ___ ___

Possibility: It might be asking for B ⊆ ? or B ∈ ?

But B is a set, not an element.

None of the given sets contain B as an element.

So B is not a subset of any of the others, nor is it an element.

But perhaps it's a typo — maybe it's asking B ⊆ ? — but none of the sets contain elements from B.

Alternatively, perhaps it's asking B ⊈ C, or B ⊈ D, etc.

But let's see pattern.

Wait — maybe it's asking for B ⊆ ? — but no such relation holds.

Alternatively, could it be that B ⊆ C? No — 2 ∉ C.

So likely, B is not a subset of any of the others.

But the blank is two underscores — probably expects a symbol and a set.

Let’s re-express:

(iv) B ___ ___

Most likely: B ⊈ C or B ⊈ D — but we don’t know which.

Wait — perhaps it's asking: B ⊆ ? — but none.

Alternatively, maybe it's B ⊂ ? — still no.

But let's think: Maybe it's asking for B ⊆ A? No.

Perhaps there's a mistake.

Wait — perhaps the intended question is: B ⊆ ? — but none of the sets include elements of B.

So perhaps the correct answer is B ⊈ C, B ⊈ D, etc.

But since only one blank, maybe it's B ⊈ C?

But let's go back.

Wait — looking at the format:

(b) Fill in the blanks:

(i) 3 ∈ ___
(ii) 4 ___ B
(iii) 26 ___ C
(iv) B ___ ___
(v) 5 ___ A
(vi) 6 ___ C
(vii) 21 ___ D
(viii) 16 ___ B

Now, (iv) has two blanks, others have one.

So likely: B ⊈ C or B ⊈ D — but which?

But B and C have no common elements.

So B ∩ C = ∅, so B is not a subset of C.

Similarly, B is not a subset of D.

But maybe it's asking: B ⊆ ? — no.

Alternatively, could it be B ⊆ {even numbers}? But not among the options.

Wait — perhaps the intended answer is: B ⊈ C — because B and C are disjoint.

But let's check if B ⊆ C? No.

So B ⊈ C — this is true.

But why C? Why not D?

Maybe the question is: B ⊈ C — so fill in: B ⊈ C

But the blank is two spaces: B ___ ___

So likely: B ⊈ C

Similarly, others:

(v) 5 ___ A
5 is in A → 5 ∈ A

(vi) 6 ___ C
6 is not in C → 6 ∉ C

(vii) 21 ___ D
21 is in D → 21 ∈ D

(viii) 16 ___ B
16 is not in B → 16 ∉ B

Now back to (iv): B ___ ___

Since B is not a subset of C, and C is a set here, and B is not contained in C, we write:

→ B ⊈ C

So the blank is: B ⊈ C

But is that the only possibility? Let's see if B is a subset of any other?

B = {2,4,6,8,10}
A = {3,5,7,9} → no
C = {12,14,18,20,24} → no
D = {21,26,31,36} → no

So B is not a subset of any of the given sets.

But perhaps the question is asking: B ⊆ ? — but no.

Alternatively, maybe it's asking: B ⊆ B — but that would be trivial.

But since B is not listed as a member of any set, we can't say B ∈ anything.

So likely, (iv) B ⊈ C — meaning B is not a subset of C.

Alternatively, maybe it's a typo and should be B ⊆ ?, but without options, we assume B ⊈ C is intended.

But let's consider: Is there any chance B is a subset of C? No.

So B ⊈ C is true.

Hence:

(iv) B ⊈ C

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✔ Final Answers for Question 2:

#### (a) True or False:

| Statement | Answer |
|---------|--------|
| (i) 13 ∈ C | False |
| (ii) 4 ∈ A | False |
| (iii) 9 ∈ A | True |
| (iv) 24 ∈ C | True |
| (v) 5 ∈ D | False |
| (vi) 36 ∈ D | True |
| (vii) 20 ∈ C | True |
| (viii) 9 ∈ A | True |

#### (b) Fill in the blanks:

| Statement | Answer |
|---------|--------|
| (i) 3 ∈ ___ | A |
| (ii) 4 ___ B | ∈ |
| (iii) 26 ___ C | ∉ |
| (iv) B ___ ___ | ⊈ C |
| (v) 5 ___ A | ∈ |
| (vi) 6 ___ C | ∉ |
| (vii) 21 ___ D | ∈ |
| (viii) 16 ___ B | ∉ |

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✔ Summary:

Q1: Only (b) and (g) are not sets due to subjectivity.

Q2(a): As above.

Q2(b): As filled.

Let me know if you'd like this formatted neatly!