Solution to Find the simplest form of given Boolean expressions using algebraic methods. i. A(A+B) + B(B+C) … - Sikademy
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Archangel Macsika

Find the simplest form of given Boolean expressions using algebraic methods. i. A(A+B) + B(B+C) + C(C+A) ii. (A+|B|)(B+C) + (A+B)(C+|A|) iii. (A+B)(AC+A|C|)_+AB +B iv. |A|(A+B) + (B+A)(A+|B|)

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(i))A(A+B)+B(B+C)+C(C+A)AA+AB+BB+BC+CC+CAA+AB+B+BC+C+CA[A.A=A,B.B=B,C.C=C]A(1+B)+B(1+C)+C(1+A)A+B+Cii)(A+Bˉ)(B+C)+(A+B)(C+Aˉ)AB+AC+BˉB+BˉC+AC+AAˉ+BC+BAˉAB+AC+O+BˉC+AC+O+BC+BAˉAB+BˉC+AC+AC+BC+BAˉAB+BˉC+AC+BC+BAˉ[AC+AC=AC]AB+BAˉ+AC+BˉC+BCB(A+Aˉ)+AC+C(Bˉ+B)B+AC+C[Aˉ+A=1]B+C(1+A)[C(1+A)=C]B+Ciii)(A+B)(AC+ACˉ)+AB+B(A+B):(A(C+Cˉ))+AB+B(A+B)A+AB+B [C+Cˉ=1]AA+BA+AB+BA+BA+AB+B[A.A=A]A(1+B)+B(1+A)A+B[A(1+B)=AB(1+A)=B]iv)Aˉ(A+B)+(B+A)(A+Bˉ)AˉA+AˉB+BA+BBˉ+AA+ABˉ0+AˉB+BA+O+A+ABˉ[AˉA=0;BBˉ=0]B(Aˉ+A)+A(1+Bˉ)B+A[Aˉ+A=1A(1+Bˉ)=A]

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