If A is a proper subset of the universal set U, which statement is correct?
Answer and explanation
Correct answer: Aᶜ ≠ ∅
A proper subset A of U is contained in U but is not equal to U. Consequently, at least one element of U is missing from A. That missing element, or those missing elements, belong to the complement Aᶜ. Hence Aᶜ must contain at least one element and cannot be empty. Also, Aᶜ is always a subset of U, so option D is false.
Frequently asked questions
What is the correct answer to this question?
Aᶜ ≠ ∅
Why is this the correct answer?
A proper subset A of U is contained in U but is not equal to U. Consequently, at least one element of U is missing from A. That missing element, or those missing elements, belong to the complement Aᶜ. Hence Aᶜ must contain at least one element and cannot be empty. Also, Aᶜ is always a subset of U, so option D is false.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
