If A = {1,2,3}, how many elements are in P(A) − {∅, A}?
Answer and explanation
Correct answer: 6
A has three elements, so its power set has 2³ = 8 elements. The power set includes both the empty set ∅ and the original set A. The expression P(A) − {∅, A} removes exactly these two distinct elements from the power set. Therefore, the remaining number of elements is 8 − 2 = 6. These remaining sets are precisely the non-empty proper subsets of A, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
A has three elements, so its power set has 2³ = 8 elements. The power set includes both the empty set ∅ and the original set A. The expression P(A) − {∅, A} removes exactly these two distinct elements from the power set. Therefore, the remaining number of elements is 8 − 2 = 6. These remaining sets are precisely the non-empty proper subsets of A, so 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.
