Let A and B be subsets of U with A union B = U. Which statement about A' is always true?
Answer and explanation
Correct answer: A' is a subset of B / A' ⊆ B
A union B = U means every element of U is in A, in B, or in both. If an element is in A', it is not in A. To still belong to U = A union B, it must therefore be in B. Hence every element of A' belongs to B, so A' is a subset of B. Equality is not guaranteed because B may contain elements that are also in A.
Frequently asked questions
What is the correct answer to this question?
A' is a subset of B / A' ⊆ B
Why is this the correct answer?
A union B = U means every element of U is in A, in B, or in both. If an element is in A', it is not in A. To still belong to U = A union B, it must therefore be in B. Hence every element of A' belongs to B, so A' is a subset of B. Equality is not guaranteed because B may contain elements that are also in A.
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.
