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Let $A,B,C$ sets. Show that $(A \cup B ) \cup C=A \cup (B \cup C)$.

That's what I have tried:

$$x \in (A \cup B) \cup C \leftrightarrow x \in A \cup B \vee x \in C \leftrightarrow x \in A \vee x \in B \vee x \in C \leftrightarrow x \in A \vee x \in B \cup C \leftrightarrow x \in A \cup(B \cup C)$$

Could you tell me if it is right?

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    $\begingroup$ Looks good to me :) $\endgroup$
    – jeanqueq
    Nov 8 '14 at 21:09
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    $\begingroup$ It's fine,but using logical connectives in such a simple proof to me is overkill. Still,if it helps you while you're learning the ropes,by all means,go for it. $\endgroup$ Nov 8 '14 at 21:19
  • $\begingroup$ Nice... Thank you!!! :-) $\endgroup$
    – evinda
    Nov 8 '14 at 22:12
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It's perfect,I'm also a a few months into set theory,and this is how I had to prove it in my homework.

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  • $\begingroup$ Great... Thank you!!! :-) $\endgroup$
    – evinda
    Nov 8 '14 at 22:12

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