Find Sets A, B and C Such That A∩B∩C = Φ
Question:
Find sets \( A \), \( B \) and \( C \) such that
\[ A\cap B,\quad A\cap C,\quad B\cap C \]are non-empty sets and
\[ A\cap B\cap C=\phi \]Solution
Consider the sets:
\[ A=\{1,2\}, \quad B=\{2,3\}, \quad C=\{1,3\} \]Now find \( A\cap B \):
\[ A\cap B=\{2\} \]So \( A\cap B \) is non-empty.
Next find \( A\cap C \):
\[ A\cap C=\{1\} \]So \( A\cap C \) is non-empty.
Now find \( B\cap C \):
\[ B\cap C=\{3\} \]So \( B\cap C \) is also non-empty.
Finally,
\[ A\cap B\cap C=\phi \]because there is no element common to all the three sets.
Hence the required sets are:
\[ A=\{1,2\}, \quad B=\{2,3\}, \quad C=\{1,3\} \]