If A ∩ B = ∅ and B ∩ C = ∅, is it necessary that A ∩ C = ∅?
Answer and explanation
Correct answer: No, A and C may overlap
The statements A ∩ B = ∅ and B ∩ C = ∅ only say that A has no common element with B and C has no common element with B. They do not compare A directly with C. For example, let A = {1}, B = {2}, and C = {1, 3}. Then both given intersections are empty, but A ∩ C = {1}, which is not empty. Therefore, A and C may overlap, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
No, A and C may overlap
Why is this the correct answer?
The statements A ∩ B = ∅ and B ∩ C = ∅ only say that A has no common element with B and C has no common element with B. They do not compare A directly with C. For example, let A = {1}, B = {2}, and C = {1, 3}. Then both given intersections are empty, but A ∩ C = {1}, which is not empty. Therefore, A and C may overlap, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
