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Answer the following in short.
Minimize: F = XY + (XZ)' + XY'Z using Boolean laws.
Minimize: $F = XY + (XZ)' + XY'Z$ using Boolean laws.
Answer
Answer
$F = XY + (XZ)' + XY'Z$
$= XY + X' + Z' + XY'Z$ (De Morgan's law on $(XZ)'$)
$= (X' + XY) + Z' + XY'Z$ (regrouping)
$= X' + Y + Z' + XY'Z$ (using $A + A'B = A + B$, i.e. $X' + XY = X' + Y$)
$= X' + Y + Z' + Y'Z$ (using $X' + XY'Z = X' + Y'Z$)
$= X' + Y + Z' + Z$ (using $Y + Y'Z = Y + Z$)
$= X' + Y + 1$ (complement law $Z + Z' = 1$)
$= 1$ (null law)
So $F = 1$ (verified with the boolean tool: the expression is a tautology).