3
$\begingroup$

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?

$\endgroup$
  • $\begingroup$ 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
0
$\begingroup$

Yes, your counterexample proves the statement is false.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.