Chapter 1: Sets

Exercise

Question

Question: 10

17 / 17

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

Answer

1
Choose three sets so that each pair shares one common element, but no element is common to all three sets.
Answer: A = {1, 2}, B = {2, 3}, C = {1, 3}
2
Verify the pairwise intersections and the intersection of all three sets.
Venn diagram showing three sets A, B, and C where each pair of sets overlaps, but no region is common to all three sets
Each pair of sets has a non-empty intersection, but the intersection of all three sets is empty.
A $∩$ B = {2} $≠$ $∅$
B $∩$ C = {3} $≠$ $∅$
A $∩$ C = {1} $≠$ $∅$
A $∩$ B $∩$ C = $∅$
Therefore, the chosen sets satisfy all the given conditions.
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