If A = {1, 2, 3}, what is the number of elements in P(A)?
Answer and explanation
Correct answer: 8
If a finite set has n elements, its power set has 2^n elements because each element has two independent choices: it may either be included in a subset or not included. Here A has n = 3 elements, so |P(A)| = 2^3 = 8. These eight subsets are the empty set, three one-element subsets, three two-element subsets, and A itself. Therefore option C is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
If a finite set has n elements, its power set has 2^n elements because each element has two independent choices: it may either be included in a subset or not included. Here A has n = 3 elements, so |P(A)| = 2^3 = 8. These eight subsets are the empty set, three one-element subsets, three two-element subsets, and A itself. Therefore option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
