1. The problem statement, all variables and given/known data Alright so I was trying to solve this using logical equivalences: Fill in the blanks to make true identities: [itex] C \backslash ( A \Delta B) = (A \cap C) \Delta [/itex] ______ I made it to the end where I stated that the missing part was (C\B), but I'm not sure if my last step was justified 2. Relevant equations Equivalences 3. The attempt at a solution [\b] I'll skip most of the steps (there were about 9) because I suck at latex but the last few are (working from the left side): [itex] [ ( x \in C \wedge x \in A) \wedge (x \notin A \vee x \in B) ] \vee [ (x \in C \wedge x \notin B) \wedge (x \notin A \vee x \in B) ] \\ [ (C \cap A) \cap (B \cup (x \notin A) ] \cap [ (C \backslash B) \cap (B \cup (x \notin A) ] \\ C \backslash (A \Delta B) = (A \cap C) \Delta (C \backslash B) [/itex] So in the 2nd to last step, I dropped [tex](B \cup (x \notin A)[/tex] from both sides of the union because of the definition of symmetric difference which says that they would be dropped even if I left them in. Is this correctly justified?