Unformatted text preview: = AB(CD)'+B'C(D'E')' = AB(C'+D')+B'C(D+E) =ABC'+ABD'+B'CD+B'CE c) F=(((A+B)'+C')'+D)' F'= ((A+B)'+C')'+D = (A+B)C+D = AC+BC+D FD= A'C'+B'C'+D' d) F=AB(C'+D')+A'B'C'+CD'(A +C') F' = (AB(C'+D'))'(A'B'C')'((CD')'+A'C) = (A'+B'+CD)(A+B+C)(C'+D+A'C) FD= (A+B+C'D')(A'+B'+C')( C+ D'+AC') 4. (6 pts with 2 pts each part) Prove the equality of the following equations and then using the principle of duality to obtain their duals. a) AB + AB'C= AB + AC PROOF: AB+AB'C = AB+ABC+AB'C = AB+AC DUAL: (A+B)(A+B'+C) = (A+B)(A+C) b) XY'+ X'Z + Y'Z=XY'+ X'Z PROOF:XY'+X'Z+Y'Z = XY'+ X'Z+XY'Z+X'Y'Z = XY'+X'Z DUAL:(X+Y')(X'+Z)(Y'+Z) = (X+Y')(X'+Z) c) (B'+C)(B'+D)=B'+CD PROOF: (B'+C)(B'+D) = B'+B'D+B'C+CD = B'+CD DUAL: B'C+B'D = B'(C+D)...
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This homework help was uploaded on 04/22/2008 for the course ECSE 2610 taught by Professor Ji during the Spring '08 term at Rensselaer Polytechnic Institute.
- Spring '08