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Which of the following are sets? (i) T...

Which of the following are sets?
(i) The collection of amazing persons in the world
(ii) The collection of all the composite numbers
(iii) The collection of all letters of the word INDIAN
(iv) The collection of all factors of 32.

Text Solution

AI Generated Solution

The correct Answer is:
To determine which of the given collections are sets, we need to analyze each option based on the definition of a set. A set is a well-defined collection of distinct elements. ### Step-by-Step Solution: 1. **Analyze the first collection: The collection of amazing persons in the world.** - The term "amazing persons" is subjective and can vary from person to person. What one individual considers amazing, another may not. Therefore, this collection does not have a clear definition and cannot be quantified or agreed upon universally. - **Conclusion:** This is **not a set**. 2. **Analyze the second collection: The collection of all composite numbers.** - Composite numbers are defined as natural numbers greater than 1 that are not prime, meaning they have more than two distinct positive divisors. Examples include 4, 6, 8, 9, 10, etc. - This collection can be clearly defined and includes distinct elements. - **Conclusion:** This is a **set**. 3. **Analyze the third collection: The collection of all letters of the word INDIAN.** - The letters in the word "INDIAN" are I, N, D, I, A, N. However, when forming a set, we only include distinct elements. Thus, we have: {I, N, D, A}. - The repetition of letters (I and N) does not affect the distinctness of the set. - **Conclusion:** This is a **set**. 4. **Analyze the fourth collection: The collection of all factors of 32.** - The factors of 32 are the numbers that divide 32 without leaving a remainder. These factors are: 1, 2, 4, 8, 16, and 32. - This collection can also be clearly defined and consists of distinct elements. - **Conclusion:** This is a **set**. ### Final Summary: - (i) Not a set - (ii) Is a set - (iii) Is a set - (iv) Is a set
To determine which of the given collections are sets, we need to analyze each option based on the definition of a set. A set is a well-defined collection of distinct elements. ### Step-by-Step Solution: 1. **Analyze the first collection: The collection of amazing persons in the world.** - The term "amazing persons" is subjective and can vary from person to person. What one individual considers amazing, another may not. Therefore, this collection does not have a clear definition and cannot be quantified or agreed upon universally. - **Conclusion:** This is **not a set**. ...
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  • Which of the following collections is a set

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