Suppose I have a sample space $S$.
I would like to check that the events $A^{c} \cap B \cap C$ and $(A^{c} \cap B \cap C)^{c}$ partition $S$, i.e. that:
1.$(A^{c} \cap B \cap C) \cap (A^{c} \cap B \cap C)^{c} = \emptyset$,
- $(A^{c} \cap B \cap C) \cup (A^{c} \cap B \cap C)^{c} = S$
I have no idea how to do this , what laws of sets would be useful here - please help.