Sets; is (A∩B)∪C the same as A∩(B∪C)?

Question

So I have this homework question, asking to prove (A∩B)∪C= (A∪C)∩(B∪C) , but that doesn't make sense to me. Shouldn't it be A∩(B∪C)= (A∪C)∩(B∪C) ?
When I check in the professors notes, that's also what it says, but I'm not sure (I'm very new to maths).
Thank you in advance for any help!

WATER · Answer

Absolutely not! There are a lot of small cases which would make this claim false, such as the suggestion by Randy Marsh:
$$ A = emptyset, C = { text{Your Choice} }$$
And knowing these facts $$ A cap emptyset = emptyset \ A cup emptyset = A$$
You would get that:
$$ ( emptyset cap B) cup C = emptyset cup C = C \ text{While:} \ A cap (B cup C) = emptyset cap (B cup C) = emptyset $$
And those are really different...
Here is a link that might help: Prove $ (A cup B) cap C$ = $(A cap C) cup (B cap C) $

Sets; is (A∩B)∪C the same as A∩(B∪C)?

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