Prove or disprove:

If $ A \nsubseteq B \cap C$, then $A \nsubseteq B$ and $A \nsubseteq C$.

I think it is false statement, shown by this counterexample:

let $A=\{1,2,3\} , B=\{1,2,3\}$, and $C=\{4,5\}$,

so $ B \cap C=\emptyset$, but $ A \subseteq B$.

Is my counterexample correct?

  • $\begingroup$ Yes, your counterexample is correct. $\endgroup$ – lulu Mar 10 '17 at 2:54
  • $\begingroup$ Yes, it works as a counterexample $\endgroup$ – Bram28 Mar 10 '17 at 2:55
  • 1
    $\begingroup$ Yes, but you don't need to mention that $A\not\subseteq C$. What you need is to mention that $A\not\subseteq B\cap C$ but $A\subseteq B$. $\endgroup$ – Juniven Mar 10 '17 at 3:01

Yes, your counterexample proves the statement is false.


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