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Prove or find a counter-example to the claim that for all sets $A,B,C$ if $A\cap B = B \cap C = A \cap C = \emptyset$, then $A \cap B \cap C=\emptyset $.

the above statement is not true so i need a counter example but i do not know to do that.i have tried but in the end i somehow get lost. please try give answer in simplest way possible. Let A={1,2,3} , B={4,5,6} and C={7,8,9}. It is then clear that A∩B=B∩C=A∩C=∅ ?

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  • $\begingroup$ is this a homework question? $\endgroup$ Apr 16, 2014 at 23:29
  • $\begingroup$ yes it is a homework question $\endgroup$
    – user129834
    Apr 16, 2014 at 23:30
  • $\begingroup$ then why did you not tag it as such? $\endgroup$ Apr 16, 2014 at 23:31
  • $\begingroup$ forgot about when i saw this question $\endgroup$
    – user129834
    Apr 16, 2014 at 23:32
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    $\begingroup$ also, please refrain from posting the question in the title. That is not what titles are for. Also, you need to use latex commands between dollar signs to make things readable. I edited your question a bit so you can see how it's done. $\endgroup$ Apr 16, 2014 at 23:32

1 Answer 1

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Let $A,B,C $ be sets. If $A \cap B = \emptyset$ then $A \cap B \cap C = (A \cap B) \cap C = \emptyset \cap C = \emptyset $. Or did i miss something?

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