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 2
 Homework Statement
 $$(A \cap B) \triangle C = (A \triangle C) \triangle (A \backslash B)$$
 Homework Equations
 none
Hello, I am having trouble with proving the following set identity:
What I did so far was focus on this:
$$((A \lor C) \land (\lnot A \lor \lnot C) \lor (A \land \lnot B)) \land ((\lnot A \land \lnot C) \lor (A \land C) \land (\lnot A \lor B))$$ > so I focus on the first part of the equation
$$((A \lor C) \land (\lnot C) \lor \lnot A \lor (A \land \lnot B)$$ which made it $$(A \land \lnot C) \lor (\lnot A \lor \lnot B)$$ and after that $$(A \land \lnot C) \lor \lnot A \lor (\lnot B)$$ which made it $$(\lnot A \lor \lnot C \lor \lnot B)$$ and using DeMorgan's Law it ended up being $$\lnot ((A \land B) \land C)) \land ???$$ I am not sure what to do for the other half of the equation though. I'm basically talking about this part:
$$((\lnot A \land \lor C) \lor (A \land C) \land (\lnot A \lor B))$$
Can someone use the same method shown in the image to the right hand side of the equation? I need help solving this and I am having a bit of trouble with this.
[Moderator's note: Moved from a technical forum and thus no template.]
$$(A \cap B) \triangle C = (A \triangle C) \triangle (A \backslash B)$$ 
$$((A \lor C) \land (\lnot A \lor \lnot C) \lor (A \land \lnot B)) \land ((\lnot A \land \lnot C) \lor (A \land C) \land (\lnot A \lor B))$$ > so I focus on the first part of the equation
$$((A \lor C) \land (\lnot C) \lor \lnot A \lor (A \land \lnot B)$$ which made it $$(A \land \lnot C) \lor (\lnot A \lor \lnot B)$$ and after that $$(A \land \lnot C) \lor \lnot A \lor (\lnot B)$$ which made it $$(\lnot A \lor \lnot C \lor \lnot B)$$ and using DeMorgan's Law it ended up being $$\lnot ((A \land B) \land C)) \land ???$$ I am not sure what to do for the other half of the equation though. I'm basically talking about this part:
$$((\lnot A \land \lor C) \lor (A \land C) \land (\lnot A \lor B))$$
Can someone use the same method shown in the image to the right hand side of the equation? I need help solving this and I am having a bit of trouble with this.
[Moderator's note: Moved from a technical forum and thus no template.]
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