If A has 3 elements, how many proper subsets does P(A) have?
Answer and explanation
Correct answer: 255
If A has 3 elements, then its power set P(A) contains 2³ = 8 elements. A set containing 8 elements has 2⁸ = 256 subsets in total. Proper subsets are all subsets except the set itself, so we must remove one subset, namely P(A) itself. Thus the number of proper subsets is 256 − 1 = 255. Therefore option B is correct. The important point is to first find the size of P(A), and only then count its subsets.
Frequently asked questions
What is the correct answer to this question?
255
Why is this the correct answer?
If A has 3 elements, then its power set P(A) contains 2³ = 8 elements. A set containing 8 elements has 2⁸ = 256 subsets in total. Proper subsets are all subsets except the set itself, so we must remove one subset, namely P(A) itself. Thus the number of proper subsets is 256 − 1 = 255. Therefore option B is correct. The important point is to first find the size of P(A), and only then count its subsets.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
