I'm working on some HW and having some trouble understanding what the question is asking. The questions is as follows:
Supply a reason for each step in the derivation. $$(A \cup B) \cap C = (A\cap C)\cup (B\cap C)$$
Proof: \begin{align*} (A \cup B) \cap C &= C \cap (A \cup B) & \text{by: (a)}\\ &= (C \cap A) \cup (C \cap B) & \text{by: (b)}\\ &= (A \cap C) \cup (B \cap C) & \text{by: (c)} \end{align*}
I understand that $C \cap (A \cup B)$ can become $(C \cap A) \cup (C \cap B)$ because of the distributive law, but I'm not sure what it means, "by: (a)".
I believe that it means that when you write your answer paper, you should say something like "(a) is the distributive law" and similarly for (b) and (c).