Assertion: (A∪B)′=A′∩B′. Reason: To be outside A∪B, an element must be outside both A and B. Choose the correct option.
Answer and explanation
Correct answer: Both assertion and reason are true, and the reason is the correct explanation
The statement is De Morgan’s law for the complement of a union. An element is outside A∪B exactly when it is not in A and also not in B. The conditions “not in A” and “not in B” describe A′ and B′, and their simultaneous occurrence is A′∩B′. Thus both the assertion and its reason are true, and the reason explains the assertion.
Frequently asked questions
What is the correct answer to this question?
Both assertion and reason are true, and the reason is the correct explanation
Why is this the correct answer?
The statement is De Morgan’s law for the complement of a union. An element is outside A∪B exactly when it is not in A and also not in B. The conditions “not in A” and “not in B” describe A′ and B′, and their simultaneous occurrence is A′∩B′. Thus both the assertion and its reason are true, and the reason explains the assertion.
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.
