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## Homework Statement

1. Provide a counterexample to the following conjecture:

For sets [tex]A, B,[/tex] [tex] C \subseteq U [/tex] if A is a subset of B but B is not a subset of C, then A is not a subset of C

2. [tex](A\cap B) \cup C = (A \cap (B \cup C))[/tex] if and only if [tex]C \subseteq A[/tex]

3. Prove [tex] (A - B) - C = (A - C) - (B - C) [/tex]

## Homework Equations

## The Attempt at a Solution

1. Would it work if I say "If [tex] \bar{A}\notin U[/tex] then [tex] A\subseteq U[/tex] and thus [tex] A \subseteq C[/tex]" ?

2. Not sure.

3. [tex] (A \cap \bar{B}) \cap \bar{C} = (A \cap \bar{C}) - (B \cap \bar{C}) [/tex]

[tex] (A \cap \bar{B}) \cap \bar{C} = (A \cap \bar{C}) \cap \bar{(B \cap \bar{C})} [/tex]

[tex] (A \cap \bar{C}) \cap (\bar{B} \cap \bar{C}) = (A \cap \bar{C}) \cap \bar{(B \cap \bar{C})} [/tex]

I'm not sure if this is right though. Can't figure out the rest of this part.