Let's solve each part of the problem step by step and determine whether each set is
empty,
singleton,
finite, or
infinite.
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a. A = {odd number between 6 and 8}
- Numbers between 6 and 8: only
7
- Is 7 odd? Yes.
- So, A = {7}
- This set has
one element.
✔ Answer: Singleton set
> Reason: A singleton set has exactly one element.
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b. B = {multiples of 5 less than 100}
- Multiples of 5: 5, 10, 15, 20, ..., 95
- All these are less than 100.
- The largest multiple of 5 less than 100 is 95.
- We can list them: 5×1, 5×2, ..., 5×19 = 95 → total of
19 elements
✔ Answer: Finite set
> Reason: The set has a limited number of elements (19), so it is finite.
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c. C = {whole numbers greater than 6}
- Whole numbers: 0, 1, 2, 3, ...
- Greater than 6: 7, 8, 9, 10, ...
- This continues indefinitely.
✔ Answer: Infinite set
> Reason: There is no end to whole numbers greater than 6; they go on forever.
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d. D = {square numbers between 10 and 15}
- Square numbers: 1, 4, 9, 16, 25, ...
- Between 10 and 15: check which squares lie in this range.
- 9 < 10 → too small
- 16 > 15 → too big
- No square number lies strictly between 10 and 15.
So, D = {} →
no elements
✔ Answer: Empty set
> Reason: No square number exists between 10 and 15.
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e. E = {letters of the word 'SCHOOL'}
- Word: S, C, H, O, O, L
- Unique letters: S, C, H, O, L
- Note: Even though 'O' appears twice, in sets, duplicates are not repeated.
- So, E = {S, C, H, O, L} →
5 elements
✔ Answer: Finite set
> Reason: It has a finite number of distinct elements.
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✔ Final Answers:
a.
Singleton set
b.
Finite set
c.
Infinite set
d.
Empty set
e.
Finite set
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Parent Tip: Review the logic above to help your child master the concept of set worksheet.
