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Prove the following identities a. A‾B‾C‾ + A‾BC‾ + AB‾C‾ + ABC‾ = C‾ b. AB + ABC + A‾ B + AB‾C = B + AC
Ans.
a. LHS = A'B'C' + A'BC' + AB'C' + ABC'= A'C' (B' + B) + AC' (B' + B)= A'C' + AC' [as B'+B = 1]= C' (A' + A)= C' [since A'+A =1]= RHS.Thus Provedb. LHS = AB + ABC + A'B + AB'C
= B + AC= B (A + A') + AC (B + B')= B + AC [as B + B' = A + A' = 1]= B + AC= RHS.Thus Proved
Q. Prove using Boolean Algebra 1. AB + AC + BC' = AC + BC' 2. (A+B+C) (A+B'+C') (A+B+C') (A+B'+C)=A 3. (A+B) (A'+B'+C) + AB = A+B 4. A'C + A'B + AB'C + BC = C + A'B
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