Find sets A, B and C such that A cap B, B cap C and A cap C are non-empty sets and A cap B cap C=ø

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1.Set Theory

easy

Find sets $A, B$ and $C$ such that $A \cap B, B \cap C$ and $A \cap C$ are non-empty sets and $A \cap B \cap C=\varnothing$

Option A

Option B

Option C

Option D

Solution

Let $A=\{0,1\}, B=\{1,2\},$ and $C=\{2,0\}$

Accordingly, $A \cap B=\{1\}, B \cap C=\{2\},$ and $A \cap C=\{0\}$

$\therefore A \cap B, B \cap C,$ and $A \cap C$ are non-empty.

Howerer, $A \cap B \cap C=\varnothing$

Standard 11

Mathematics

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