If A and B are subsets of a universal set U and A is a subset of B, which of the following statements is always true?
Answer and explanation
Correct answer: B′ ⊆ A′
Since A ⊆ B, every element of A is also an element of B. Therefore, if an element is not in B, it cannot be in A. The elements outside B are consequently contained among the elements outside A, giving B′ ⊆ A′. Complementation reverses the direction of a subset relation; this is a fundamental property of complements.
Frequently asked questions
What is the correct answer to this question?
B′ ⊆ A′
Why is this the correct answer?
Since A ⊆ B, every element of A is also an element of B. Therefore, if an element is not in B, it cannot be in A. The elements outside B are consequently contained among the elements outside A, giving B′ ⊆ A′. Complementation reverses the direction of a subset relation; this is a fundamental property of complements.
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.
