Question

prove that (ABC)'+(AB)'C+A'BC'+A(BC)'+AB'C=(ABC)'​

Answer 1

Answer:

It’s actually easier to show what happens in reverse (i.e., go from the simplified expression to the original version), so here we go:

AB+AC+BC=

Using X1=X

AB1+A1C+1BC=

Using 1=X+X′

AB(C+C′)+A(B+B′)C+(A+A′)BC=

Using X(Y+Z)=XY+XZ

ABC+ABC′+ABC+AB′C+ABC+A′BC=

Using X+X=X

ABC+ABC′+AB′C+A′BC=

QED

Note: implicitly the rules for associativity ( X(YZ)=(XY)Z and X+(Y+Z)=(X+Y)+Z ) and commutativity ( XY=YX , X+Y=Y+X ) are also being used.

Hope it helps to u....