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The number of subsets of a set containing n elements is
- a)2n
- b)2–n
- c)n
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The number of subsets of a set containing n elements isa)2nb)2–n...
Explanation:
To understand the concept of subsets, let's first understand what a subset is.
Subset: A subset is a set that contains elements from another set, which is called the superset.
For example, let's say we have a set A = {1, 2, 3}. The possible subsets of this set are:
- {} (empty set)
- {1}
- {2}
- {3}
- {1,2}
- {1,3}
- {2,3}
- {1,2,3}
Counting the number of subsets:
To count the number of subsets of a set containing n elements, we can use the following formula:
Number of subsets = 2^n
Let's take the example of the set A = {1, 2, 3}. Here, n = 3. Using the formula above, we get:
Number of subsets = 2^3 = 8
As we saw earlier, the possible subsets of set A were also 8. Hence, the formula is correct.
Therefore, the correct answer is option 'A', i.e., 2^n.
To understand the concept of subsets, let's first understand what a subset is.
Subset: A subset is a set that contains elements from another set, which is called the superset.
For example, let's say we have a set A = {1, 2, 3}. The possible subsets of this set are:
- {} (empty set)
- {1}
- {2}
- {3}
- {1,2}
- {1,3}
- {2,3}
- {1,2,3}
Counting the number of subsets:
To count the number of subsets of a set containing n elements, we can use the following formula:
Number of subsets = 2^n
Let's take the example of the set A = {1, 2, 3}. Here, n = 3. Using the formula above, we get:
Number of subsets = 2^3 = 8
As we saw earlier, the possible subsets of set A were also 8. Hence, the formula is correct.
Therefore, the correct answer is option 'A', i.e., 2^n.
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Community Answer
The number of subsets of a set containing n elements isa)2nb)2–n...
- A set with n elements can have subsets of varying sizes, from the empty set to the full set itself.
- For each element in the set, there are two choices: include it in a subset or not.
- Therefore, each element's inclusion or exclusion doubles the number of possible subsets.
- Mathematically, this results in 2^n total subsets.
- This is why the correct answer is 2^n, which corresponds to option A.
- For each element in the set, there are two choices: include it in a subset or not.
- Therefore, each element's inclusion or exclusion doubles the number of possible subsets.
- Mathematically, this results in 2^n total subsets.
- This is why the correct answer is 2^n, which corresponds to option A.
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