Answer to Question #276381 in Electric Circuits for slejs

Question #276381

Simplification theorems (Boolean)

1. X+XY=X

2.X(X+Y)=X

3.(X+Y')Y=XY


1
Expert's answer
2021-12-07T20:15:35-0500

(1)

X+XY =X

LHS

X+XY =X(1+Y)

Where 1+Y=1


X+XY=X(1+Y)=X×1=XX+XY=X(1+Y)=X\times1=X

X+XY=XX+XY=X

LHS=RHS

(2)

X(X+Y)=X

LHS

X(X+Y)=X×X+X×YX(X+Y)=X\times X+X\times Y

XX=X

X(X+Y)=X+XYX(X+Y)=X+XY

X(X+Y)=X(1+Y)X(X+Y)=X(1+Y)

Where 1+Y=1

X(X+Y)=X×1X(X+Y)=X\times1

X(X+Y)=X

LHS=RHS

(3)

(X+Y')Y=XY

LHS

(X+Y')Y=XY+YY'

Where YY'=0

(X+Y')Y=XY+0

(X+Y')Y=XY

LHS =RHS




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