Let A and B be two sets in a universal set U. Which of the following statements is always true?
Answer and explanation
Correct answer: If A ⊆ B, then B′ ⊆ A′
When A ⊆ B, every element of A is also an element of B. Therefore, any element that is outside B must certainly be outside A. This means B′ ⊆ A′. Complementation reverses the direction of subset inclusion. The other statements are not always true: for example, A′ ∩ B′ equals (A ∪ B)′, not necessarily the empty set.
Frequently asked questions
What is the correct answer to this question?
If A ⊆ B, then B′ ⊆ A′
Why is this the correct answer?
When A ⊆ B, every element of A is also an element of B. Therefore, any element that is outside B must certainly be outside A. This means B′ ⊆ A′. Complementation reverses the direction of subset inclusion. The other statements are not always true: for example, A′ ∩ B′ equals (A ∪ B)′, not necessarily the empty set.
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.
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