If A = {1, 2, 3, 4}, how many elements of P(A) are disjoint from A?
Answer and explanation
Correct answer: 1
An element of P(A) is itself a subset X of A. Since X ⊆ A, we have X ∩ A = X. For this intersection to be empty, X must be the empty set ∅. Thus the only member of P(A) disjoint from A is ∅, so the number is 1. Although P(A) has 2⁴ = 16 members, every non-empty subset shares at least one element with A. Therefore option B is correct.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
An element of P(A) is itself a subset X of A. Since X ⊆ A, we have X ∩ A = X. For this intersection to be empty, X must be the empty set ∅. Thus the only member of P(A) disjoint from A is ∅, so the number is 1. Although P(A) has 2⁴ = 16 members, every non-empty subset shares at least one element with A. Therefore option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
