If A = {x, y, z, w}, how many elements of P(A) are not proper subsets of A?
Answer and explanation
Correct answer: 1
The power set P(A) contains every subset of A, including A itself. A proper subset must be strictly smaller than the original set, so A is not a proper subset of itself. Every other subset of A has fewer than four elements and is proper. Thus exactly one element of P(A), namely A, is not a proper subset. The answer is option B.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
The power set P(A) contains every subset of A, including A itself. A proper subset must be strictly smaller than the original set, so A is not a proper subset of itself. Every other subset of A has fewer than four elements and is proper. Thus exactly one element of P(A), namely A, is not a proper subset. The answer is option B.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
