If A = {1, 2, 3, 4}, how many elements does P(A) have?
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Answer and explanation
Correct answer: 16
The power set P(A) is the collection of all subsets of A. If a set has n elements, each element has two choices—being included or excluded—so the power set has 2^n elements. Here n = 4, giving |P(A)| = 2^4 = 16. Therefore, option C is correct. The value 4 is the size of A itself, not the size of its power set.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The power set P(A) is the collection of all subsets of A. If a set has n elements, each element has two choices—being included or excluded—so the power set has 2^n elements. Here n = 4, giving |P(A)| = 2^4 = 16. Therefore, option C is correct. The value 4 is the size of A itself, not the size of its power set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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