Let A, BCU. Complete the following proof of the statement given below. (AUB) n (AUB) ≤ A, where Bº = U\B. Proof: By distributivity of disjunction with respect to conjunction, and x € (AUB) n(AU Bº) ⇒ (x ¤ An (AUB)) Since An A= Now, since BnB = TE ((ANA) U (An Bº)) Since An BCA, Thus, Since An BCA and AUA = A, Then since (An B) u0= TE( _U(An Bº)) U ((B^ A) u (B^ Bº)). x € (AU (ANB)) U ((BNA) U AU (ANB) C TEAU( ((BNA) U (Bn B°)). x EAUA = (Bn(AUB)), (AUB) n (AUB) ≤ A

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