NCERT Solutions, CBSE Sample Papers and Syllabus for Class 9 to 12 : Find sets A, B and C such that A ∩ B, B ∩ C and A ∩ C are non-empty sets and A ∩ B ∩ C = Φ.

Tuesday 15 April 2014

Find sets A, B and C such that A ∩ B, B ∩ C and A ∩ C are non-empty sets and A ∩ B ∩ C = Φ.

Answer
Let take three set A = {1, 2}, B = {2, 3}, and C = {3, 1}.
A ∩ B, B ∩ C and A ∩ C should be non-empty sets
A ∩ B = {2}, B ∩ C = {3}, and A ∩ C = {1}.
Therefore A ∩ B, B ∩ C, and A ∩ C are non-empty.
Intersection of all three sets is null set, A ∩ B ∩ C = Φ.