Practice worksheet Set Theory- Class vii - Math with JM - home - Free Printable

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.

We need to determine whether each collection is a set or not.
A set is a well-defined collection of distinct objects. For something to be a set, its elements must be clearly defined and distinguishable — no ambiguity in membership.

#### (a) The collection of all the days in a week beginning with the letter "T".

- Days starting with "T": Tuesday, Thursday.
- This is well-defined: only two such days exist.
✔ This is a set.

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

- "Difficult" is subjective — one person may find a question hard, another may not.
- There's no clear criterion for inclusion.
✘ Not a set, because it's not well-defined.

#### (c) The collection of girls in your class.

- Assuming we know which class we're referring to, the girls can be clearly identified.
- Each girl either is or isn't in the class.
✔ This is a set.

#### (d) The collection of all rivers in India.

- Rivers in India can be listed and identified clearly (e.g., Ganga, Yamuna, etc.).
- Though large, it’s well-defined.
✔ This is a set.

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

- "Active" might be ambiguous — does it mean currently teaching, employed, or working full-time?
- But assuming we define “active” as currently employed and teaching, it could be well-defined.
- In context, this is likely considered well-defined if the school records are known.
✔ This is a set (assuming clear definition of "active").

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

- Integers greater than -3: -2, -1, 0, 1, 2, 3, ...
- This is well-defined — any integer can be checked against the condition.
✔ This is a set.

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

- "Beautiful" is subjective — depends on personal opinion.
- No objective criterion.
✘ Not a set, because it's not well-defined.

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✔ Summary for Question 1:

| Item | Is it a set? | Justification |
|------|--------------|-------------|
| (a) | Yes | Only Tuesday and Thursday — well-defined |
| (b) | No | "Difficult" is subjective |
| (c) | Yes | Clearly identifiable individuals |
| (d) | Yes | Well-known list of rivers |
| (e) | Yes | If "active" is clearly defined |
| (f) | Yes | Clear mathematical condition |
| (g) | No | "Beautiful" is subjective |

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Question 2: Given sets

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

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

We check if each element belongs to the given set.

(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 = {3, 5, 7, 9} → 9 is in A
✔ True

(iv) 24 ∈ C
C = {12, 14, 18, 20, 24} → 24 is in C
✔ True

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

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

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

(viii) 9 ∈ A
Already done: yes
✔ True

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#### (b) Fill in the blanks

Use symbols: ∈ (belongs to), ∉ (does not belong to), ⊆ (subset), ⊈ (not subset)

(i) 3 ∈ ___
3 is in A → 3 ∈ A
Answer: A

(ii) 4 ___ B
4 is in B → 4 ∈ B
Answer: ∈

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

(iv) B ___ ___
We are to fill: B ___ ?
Looking at options: compare B and others.

B = {2, 4, 6, 8, 10}
Is B a subset of any other set?

- C = {12, 14, 18, 20, 24} → no common elements → B ⊈ C
- D = {21, 26, 31, 36} → no overlap → B ⊈ D
- A = {3,5,7,9} → no overlap

So B is not a subset of any other given set.

But perhaps they want us to write B ⊆ B? That’s always true.

Wait — maybe the blank is for relation between B and another set?

But the format says:
(iv) B ___ ___ → probably meant to be: B ___ [some set]

Looking back:
"(iv) B ___ ___" — seems like a typo or formatting issue.

Possibly it should be:
(iv) B ___ C or similar.

But since it's written as "B ___ ___", maybe it's asking for a relation like "B ⊆ C"? But that’s false.

Alternatively, perhaps it's asking for:
"B ___ A" → but no.

Wait — let's look at the pattern:

(i) 3 ∈ ___ → so fill in the set
(ii) 4 ___ B → fill in ∈ or ∉
(iii) 26 ___ C → ∉
(iv) B ___ ___ → likely missing set name.

But from context, possibly it's:
(iv) B ⊆ C? → False
(iv) B ⊆ D? → False
(iv) B ⊆ A? → False
None are subsets.

But what about B ⊆ B? Always true.

But that would be: B ⊆ B → but the blank is two underscores.

Alternatively, maybe it's a typo and it's meant to be:

(iv) B ⊆ ___ → then we can say B ⊆ B

But B is not a subset of C, D, A.

Wait — maybe it's asking for which set contains B?

But none do.

Alternatively, maybe it's asking:
(iv) B ___ ___ → meaning "B is a subset of ___"

But no set contains B.

Wait — perhaps it's a mistake.

Another idea: maybe it's asking for what set B is a subset of — but none.

Wait — look at the numbers again.

B = {2,4,6,8,10} — even numbers from 2 to 10.

C = {12,14,18,20,24} — even numbers, but larger.

No overlap.

So B is not a subset of any other given set.

But perhaps the question is:
(iv) B ___ ___ → maybe it's B ⊆ B → so fill in ⊆ and B?

But that seems odd.

Wait — looking at the structure:

Let’s assume the intended format is:

(iv) B ___ C → then we fill in ⊈ (not subset)

But it's written as "B ___ ___" — two blanks.

Perhaps it's:
(iv) B ___ ___ → meaning "B is a subset of ___" → then answer: B ⊆ B

So: ⊆ B

But that feels forced.

Alternatively, maybe it's:
(iv) B ___ A → then fill in ⊈

But again, two blanks.

Wait — let's skip and go to next.

(v) 5 ___ A
5 is in A → 5 ∈ A
Answer: ∈

(vi) 6 ___ C
6 is not in C → 6 ∉ C
Answer: ∉

(vii) 21 ___ D
21 is in D → 21 ∈ D
Answer: ∈

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

Now going back to (iv):
(iv) B ___ ___

Possibility: It might be a typo, and should be:
(iv) B ⊆ ___ → then answer: B ⊆ B → so fill in ⊆ and B

Or:
(iv) B ___ C → then answer: B ⊈ C

But since it's two blanks, maybe it's:
B ⊈ C → so first blank: ⊈, second: C

That makes sense.

Similarly, in (v) it's 5 ___ A → one blank → ∈

So (iv) has two blanks → likely: B ⊈ C

Because B and C have no common elements → B is not a subset of C.

Similarly, B is not a subset of D or A.

So likely:
(iv) B ⊈ C → so fill in: ⊈ and C

But why C? Why not D?

But C is the only set that has even numbers, but different range.

But B and C are both even numbers, but B is smaller.

But still, no overlap.

So B ⊈ C → correct.

Alternatively, maybe it's asking: B ___ ___ → meaning "B is a subset of ___" → but no.

Given the pattern, I think the most plausible interpretation is:

(iv) B ⊈ C → so fill in: ⊈ and C

But let's see if there's another possibility.

Wait — perhaps the question is:

(iv) B ___ ___ → and we are to write: B ⊆ B → so ⊆ and B

But that would be redundant.

Alternatively, maybe it's:
(iv) B ⊆ ___ → and answer: B ⊆ B → so fill in ⊆ and B

But the blank is two underscores, so maybe: ⊆ and B

Yes — possible.

But in standard notation, we don’t usually write "B ⊆ B" unless asked.

But let's consider the context.

Looking at (v): 5 ___ A → ∈ → one blank

(vi): 6 ___ C → ∉ → one blank

So (iv) has two blanks → likely: B ⊈ C or B ⊆ B

But "B ⊆ B" is trivial.

Alternatively, maybe it's a typo and should be:

(iv) B ⊆ C → then answer: ⊈

But written as two blanks.

I think the best bet is:

(iv) B ⊈ C → so first blank: ⊈, second: C

Because B and C are both sets of even numbers, and students might think they’re related, but they aren't.

So likely, the intended answer is:

(iv) B ⊈ C

So fill in: ⊈ and C

But to confirm: is there any chance B ⊆ C? No — 2,4,6,8,10 are not in C.

So B ⊈ C

✔ So answer: ⊈, C

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Final Answers:

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Question 1: Which are sets?

| Item | Answer | Reason |
|------|--------|--------|
| (a) | Yes | Well-defined: Tuesday, Thursday |
| (b) | No | "Difficult" is subjective |
| (c) | Yes | Girls in class are identifiable |
| (d) | Yes | Rivers in India are well-defined |
| (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(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 |

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Question 2(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 | ∉ |

> Note: For (iv), assuming the intended meaning is "B is not a subset of C", so fill in ⊈ and C.

If the worksheet meant something else (like B ⊆ B), it would be ⊆ and B, but that seems less likely in context.

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✔ Final Answer Summary:

Q1:
(a) Yes
(b) No
(c) Yes
(d) Yes
(e) Yes
(f) Yes
(g) No

Q2(a):
(i) False
(ii) False
(iii) True
(iv) True
(v) False
(vi) True
(vii) True
(viii) True

Q2(b):
(i) A
(ii) ∈
(iii) ∉
(iv) ⊈, C
(v) ∈
(vi) ∉
(vii) ∈
(viii) ∉

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