If U is the universal set, then (A ∩ B')' is equal to which of the following?
Answer and explanation
Correct answer: A' ∪ B
Apply De Morgan’s law to the intersection: (X ∩ Y)' = X' ∪ Y'. Here, X = A and Y = B'. Thus, (A ∩ B')' = A' ∪ (B')'. The complement of a complement returns the original set, so (B')' = B. Therefore, (A ∩ B')' = A' ∪ B, which is option A. This result also agrees with the element-wise interpretation: an element is outside A ∩ B' whenever it is outside A or it belongs to B.
Frequently asked questions
What is the correct answer to this question?
A' ∪ B
Why is this the correct answer?
Apply De Morgan’s law to the intersection: (X ∩ Y)' = X' ∪ Y'. Here, X = A and Y = B'. Thus, (A ∩ B')' = A' ∪ (B')'. The complement of a complement returns the original set, so (B')' = B. Therefore, (A ∩ B')' = A' ∪ B, which is option A. This result also agrees with the element-wise interpretation: an element is outside A ∩ B' whenever it is outside A or it belongs to B.
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.
