Let's say you have sets $A,\, B,$ and $C.$
How would you show that $[(A-B) - C]\subseteq (A-C)$ using a venn diagram or logical translations?
How can this even be done when you don't know the members of $A,\, B,$ or $C$?
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You'd need to use logical translations, implicitly (no need for logic symbols though - words work fine), in the sense that you need to use the definition of set-minus where $\;x \in X - Y\;$ means that $\;x \in X\;$ AND $\,x \notin Y.$
Showing that set-membership in $\,X\,$ implies set-membership in $\,Y,\,$ proves that $\,X\subseteq Y$. Logically, this is establishing that $\,x \in [(A - B) - C] \implies x \in (A - C).$
In this case, start by assuming $\,x \in (A - B) - C,\,$ and then unpack what this means using the definition of set-minus. Using this you can argue that it must follow that $\,x \in A-C.\,$ This is equivalent to proving that $\,(A-B) -C \subseteq A - C$.