$[6]$ Using properties of Boolean algebra, simplify the following Boolean expressions so they could be built with the minimum number of gates.

$2$

a$.x=A+BC+AB+$ABC$+B$

b$.Y=AB+B(AC+BC+AB{C}^{\text{'}}+A)$

c$.Z=A{B}^{\text{'}}+(A^{\text{'}}{B}^{\text{'}}+B{C}^{\text{'}}{)}^{\text{'}}+(A^{\text{'}}+C{)}^{\text{'}}$

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