Given: F(A,B,C) = A’B + AB’ and G(A,B,C) = A’BC’ + AB’C’ + A’BC...

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Question

Given: F(A,B,C) = A’B + AB’ and G(A,B,C) = A’BC’ + AB’C’ + A’BC...

Given: F(A,B,C) = A’B + AB’

and G(A,B,C) = A’BC’ + AB’C’ + A’BC + AB’C

Prove that F(A,B,C) = G(A,B,C)

engineering Computer-Science

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Answer 1

Answer #1

F(A,B,C)
= A’B + AB’
Applying identity law
= A’B + AB’(1)
Applying inverse law
= A’B + AB’(C’+C)
Applying distributive law
= A’B + AB’C’ + AB’C
Applying identity law
= A’B(1) + AB’C’ + AB’C
Applying inverse law
= A’B(C’+C) + AB’C’ + AB’C
Applying distributive law
= A’BC’ + AB’C’ + A’BC + AB’C
= G(A,B,C)

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Answer 2

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