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Convert the following expression into its canonical POS form:
Convert the following expression into its canonical POS form:
$F(X, Y, Z) = (X+Y' ) \cdot (Y'+Z)$
Answer
Answer
AI$F(X,Y,Z) = (X+Y').(Y'+Z)$
Each term is expanded to include the missing variable by ORing it with (variable.variable'):
$(X+Y') = (X+Y'+Z.Z') = (X+Y'+Z).(X+Y'+Z')$
$(Y'+Z) = (Y'+Z+X.X') = (X+Y'+Z).(X'+Y'+Z)$
Combining and removing the repeated term $(X+Y'+Z)$:
Canonical POS: $F(X,Y,Z) = (X+Y'+Z).(X+Y'+Z').(X'+Y'+Z)$
(verified with the boolean tool)
From ISC 2018 Computer Science Paper 1, question 1(b).