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Question
Find sets A, B and C such that \[A \cap B, A \cap C \text{ and } B \cap C\]are non-empty sets and\[A \cap B \cap C = \phi\]
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Solution
Let us consider the following sets,
A = {5, 6, 10 }
B = {6,8,9}
C = {9,10,11}
\[\text{ Clearly }, A \cap B = \left\{ 6 \right\}\]
\[B \cap C = \left\{ 9 \right\}, A \cap C = \left\{ 10 \right\} \text{ and } A \cap B \cap C = \phi\]
\[\text{ It means that }, A \cap B, B \cap C \text{and}] A \cap C \text{ are non empty sets }\]
\[\text{ and } A \cap B \cap C = \phi\]
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