Table 3.5.1: Set identities. Name Idempotent laws Associative laws Commutative laws Distributive laws Identity laws Domination laws Double complement law Complement laws De Morgan's laws Absorption laws AUA-A (AUB) UC-AU (BUC) AUB-BUA Identities AU (BOC)-(AUB) n (AU (C)=(A AUØ-A ANGIO AnA=0 UIØ AUB-ANB AU (ANB)-A ΑΠΑΞΑ (ANB) NC-An (BNC) ANB-BNA An (Buc)-(ANB) u (AN C) ANU-A AUU-U A -A AUA-U O=U ANB-AUB AN (AUB)-A The set subtraction law states that A - B = An B. Use the set subtraction law as well as the other set identities given in the table above to prove each of the following new identity. Label each step in your proof with the set identity used to establish that step. Prove: A-(BA) = A - B

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Intelligent Machines

Machines that use artificial intelligence to learn from the environment and past experiences to perform better in the presence of variability and uncertainty are called intelligent machines. Intelligence develops according to environment and experience. It is human-like behavior. When the computer system or any programmed machine learns from the inputs and corresponding outputs, it can be called an intelligent machine.