Question

Convert the following expression into its canonical POS form:  

F(X, Y, Z) = (X + Y) . (Y’ + Z)

Answer 1

F(X, Y, Z) = (X + Y’).(Y’ + Z) 

By De-Morgan’s theorem, we have 

((X + Y’).(Y’ + Z))’ 

= (X + Y’)’ + (Y’+ Z)’ 

=X’.Y” + Y”.Z’ = X’.Y + Y.Z’ 

= Y.(X’ + Z’) 

Again applying De-Morgan’s theorem, we have 

(Y.(X’ + Z’))’ = (X’ + Z’)’