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Order of the power set P(A) of a set A of order n is equal to:
- a)n
- b)2n
- c)2n
- d)n2
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Order of the power set P(A) of a set A of order n is equal to:a)nb)2nc...
The cardinality of the power set is equal to 2n, where n is the number of elements in a given set.
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Order of the power set P(A) of a set A of order n is equal to:a)nb)2nc...
Understanding the Power Set
The power set, denoted as P(A), is the set of all possible subsets of a set A. If A has n elements, the power set contains every possible combination of those elements, including the empty set and A itself.
Order of the Power Set
The order of a set refers to the number of elements in that set. For the power set P(A):
- Each element in the original set A can either be included in a subset or not.
- Therefore, for each of the n elements, there are 2 choices (include or exclude).
Calculating the Number of Subsets
The total number of subsets can be calculated as follows:
- For n elements, the number of subsets is given by:
- \(2^n\)
- This means that the power set P(A) will contain \(2^n\) subsets.
Conclusion on the Order of P(A)
Since the order of the power set P(A) is the number of subsets:
- The order of P(A) is \(2^n\).
Thus, the correct answer is option C) \(2^n\).
The power set, denoted as P(A), is the set of all possible subsets of a set A. If A has n elements, the power set contains every possible combination of those elements, including the empty set and A itself.
Order of the Power Set
The order of a set refers to the number of elements in that set. For the power set P(A):
- Each element in the original set A can either be included in a subset or not.
- Therefore, for each of the n elements, there are 2 choices (include or exclude).
Calculating the Number of Subsets
The total number of subsets can be calculated as follows:
- For n elements, the number of subsets is given by:
- \(2^n\)
- This means that the power set P(A) will contain \(2^n\) subsets.
Conclusion on the Order of P(A)
Since the order of the power set P(A) is the number of subsets:
- The order of P(A) is \(2^n\).
Thus, the correct answer is option C) \(2^n\).
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Order of the power set P(A) of a set A of order n is equal to:a)nb)2nc)2nd)n2Correct answer is option 'C'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about Order of the power set P(A) of a set A of order n is equal to:a)nb)2nc)2nd)n2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Order of the power set P(A) of a set A of order n is equal to:a)nb)2nc)2nd)n2Correct answer is option 'C'. Can you explain this answer?.
Order of the power set P(A) of a set A of order n is equal to:a)nb)2nc)2nd)n2Correct answer is option 'C'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about Order of the power set P(A) of a set A of order n is equal to:a)nb)2nc)2nd)n2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Order of the power set P(A) of a set A of order n is equal to:a)nb)2nc)2nd)n2Correct answer is option 'C'. Can you explain this answer?.
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