To prove the identity (A-B)-C=A-(B∪C), the discussion highlights the use of set identities, specifically A-B=A\bar{B} and \overline{B∪C}=\bar{B}\bar{C}. The proof involves manipulating these identities to show the equivalence. The conversation emphasizes the importance of understanding set operations and their properties, including commutativity and associativity. Participants are encouraged to apply the provided identities to validate the equality. This exploration of set theory identities is crucial for grasping advanced concepts in mathematics.