If A ∩ B = A ∩ B', which conclusion must be true?
Answer and explanation
Correct answer: A = ∅
B and B' are disjoint because no element can simultaneously belong to a set and its complement. Consequently, A ∩ B and A ∩ B' are also disjoint. The question states that these two disjoint sets are equal. The only set equal to two disjoint copies of itself is the empty set, so A ∩ B = A ∩ B' = ∅, which forces A = ∅.
Frequently asked questions
What is the correct answer to this question?
A = ∅
Why is this the correct answer?
B and B' are disjoint because no element can simultaneously belong to a set and its complement. Consequently, A ∩ B and A ∩ B' are also disjoint. The question states that these two disjoint sets are equal. The only set equal to two disjoint copies of itself is the empty set, so A ∩ B = A ∩ B' = ∅, which forces 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.
