If A = {1, 2, 3}, how many elements does its power set P(A) contain?
Answer and explanation
Correct answer: 8
The set A contains three elements. For any finite set with n elements, the power set contains 2^n elements, because every element has two choices: it may be included in a subset or excluded. Thus, |P(A)| = 2^3 = 8. Therefore, the power set has eight elements, and option B is correct. The value 3 is the number of elements of A, not of its power set.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The set A contains three elements. For any finite set with n elements, the power set contains 2^n elements, because every element has two choices: it may be included in a subset or excluded. Thus, |P(A)| = 2^3 = 8. Therefore, the power set has eight elements, and option B is correct. The value 3 is the number of elements of A, not 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.
