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: 7
- Is 7 odd? Yes.
- So, A = {7}
- This set has
one element.
✔ Answer: Singleton set
> *Reason:* A singleton set contains exactly one element.
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b. B = {multiples of 5 less than 100}
- Multiples of 5: 5, 10, 15, 20, ..., 95
- The largest multiple of 5 less than 100 is 95.
- So, this list is finite: from 5 to 95 in steps of 5.
- Number of elements: (95 - 5)/5 + 1 = 19 elements
✔ Answer: Finite set
> *Reason:* There are a limited number of multiples of 5 less than 100.
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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 upper limit; infinitely many whole numbers exist greater than 6.
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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
- So, no square number lies strictly between 10 and 15.
✔ Answer: Empty set
> *Reason:* No elements satisfy the condition.
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e. E = {letters of the word 'SCHOOL'}
- Word: S, C, H, O, O, L
- Set contains unique letters only (no repetition).
- So, E = {S, C, H, O, L}
- Count: 5 distinct letters
✔ Answer: Finite set
> *Reason:* It has a fixed, countable number of elements (5).
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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 sets worksheet.
