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ACT Exam  >  ACT Questions  >  Order of the power set P(A) of a set A of ord... Start Learning for Free
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?
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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) \(2^n\).
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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?
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