Problem $1(15$ points$)$ Simplify the following Boolean expressions to a minimum number of literals by

employing the axiom$($s$)$ and$/$or theorem$($s$)$ of Boolean algebra:

a$.$ ABC$+A^{\text{'}}B+$ABC,

b$.(B{C}^{\text{'}}+A^{\text{'}}D)(A{B}^{\text{'}}+C{D}^{\text{'}})$

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