$3-3.$ Obtain the simplified expressions in sum of products for the following Boolean

functions:

$($a$)D(A^{\text{'}}+B)+B^{\text{'}}(C+AD)$

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

$($c$)k^{\text{'}}l{m}^{\text{'}}+k^{\text{'}}{m}^{\text{'}}n+kl{m}^{\text{'}}{n}^{\text{'}}+lm{n}^{\text{'}}$

$($d$)A^{\text{'}}{B}^{\text{'}}{C}^{\text{'}}{D}^{\text{'}}+A{C}^{\text{'}}{D}^{\text{'}}+B^{\text{'}}C{D}^{\text{'}}+A^{\text{'}}BCD+B{C}^{\text{'}}D$

$($e$)x^{\text{'}}z+w^{\text{'}}x{y}^{\text{'}}+w(x^{\text{'}}y+x{y}^{\text{'}})$