(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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# Homework Help: Set Equivalencies and stuff

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