If A = {1, 2, 3}, how many elements does P(A), the power set of A, have?
Answer and explanation
Correct answer: 8
The power set P(A) contains every subset of A, including the empty set and A itself. If a set has n elements, its power set has 2^n elements because each original element can either be included or excluded from a subset. Here n = 3, so |P(A)| = 2³ = 8. Therefore, option C is correct; 3 counts elements of A, not its subsets.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The power set P(A) contains every subset of A, including the empty set and A itself. If a set has n elements, its power set has 2^n elements because each original element can either be included or excluded from a subset. Here n = 3, so |P(A)| = 2³ = 8. Therefore, option C is correct; 3 counts elements of A, not its subsets.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
