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tux
Prove using set identities: (A∩B)U(A∩B^c)=A
\[ \large (A\cap B)\cup(A\cap B^c)=A\cap(B\cup B^c)=A\cap U=A \] where \(U\) is "the/a universe".
Is this your first step? \[(A \cup A) \cap (A \cup B ^{c}) \cap (B \cup A) \cap (B \cup B^c)\]