2
$\begingroup$

Prove: if $A \subseteq C$ and $B \subseteq C$, then $A \cup B \subseteq C$

It's quite obvious, but I'm not sure what the proper approach is to proving a set problem that involves subsets, as none of the set identities given in our textbook include subsets.

$\endgroup$
3
$\begingroup$

Usually what you want to do is pick any arbitrary element of $A \cup B$, call it $x$. So $x \in A \cup B$. Then show that $x \in C$, using what you know about elements of $A$ and $B$.

$\endgroup$
4
$\begingroup$

To show $A\cup B \subseteq C$, we show that for any $x \in A\cup B$, it follows that $x \in C$.


Assumptions (Givens): $A\subseteq C$, $B \subseteq C$.

Suppose $x \in A\cup B.\;\;$ Then $x \in A$, or $x\in B\;$ (from the definition of set union).

Now, use what you know from our givens above to argue, therefore, $x \in C$.

Thus, we will have shown $A\cup B \subseteq C$.

$\endgroup$

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.