Using the basic identities of sets, establish the identity [C ∩ (A ∪ B)] ∪ [(A ∪ B) ∩ C ′] = A ∪ B.

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Prove that $[C \cap (A \cup B)] \cup [(A \cup B) \cap C^{\prime}] = A ∪ B$.

I arrived at a part of the proof where "$C^{\prime} \cap A$". Would the answer to that be "$A$" or "$\emptyset$"? I'm not sure about the answer to that.