1
$\begingroup$

Sorry for the childish question. I know that

$$ (A\cup B) \cap C = (A \cap C) \cup (B \cap C) $$

and that when we have only unions or intersections the brackets don't really matter, so I guess what I'm really asking is are $$ A \cup B \cup C $$ and $$ (A \cup B) \cup C = (A \cup C) \cup (B \cup C) $$ one and the same?

$\endgroup$
3
$\begingroup$

Yes, by idempotent/associative/commutative law: \begin{align*} A \cup B \cup C &= (A \cup B) \cup C \\ &= (A \cup B) \cup (C \cup C) \\ &= A \cup (B \cup C) \cup C \\ &= A \cup (C \cup B) \cup C \\ &= (A \cup C) \cup (B \cup C) \\ \end{align*}

$\endgroup$

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.