Simplify each of the following expressions by applying only the stated theorem or law.

$($a$)$ Complementarity law: $(x+Y^{\text{'}}Z)+(x+Y^{\text{'}}Z{)}^{\text{'}}$

$($b$)$ Uniting theorem: $[W+x^{\text{'}}(Y+Z)][W^{\text{'}}+x^{\text{'}}(Y+Z)]$

$($c$)$ Elimination theorem: $(V^{\text{'}}W+Ux{)}^{\text{'}}(Ux+Y+Z+V^{\text{'}}W)$

$($d$)$ Absorption theorem: $(U{V}^{\text{'}}+W^{\text{'}}x)(U{V}^{\text{'}\text{'}}+W^{\text{'}}x+Y^{\text{'}}Z)$

$($e$)$ Uniting theorem: $(W^{\text{'}}+x)(Y+Z^{\text{'}})+(W^{**}+x{)}^{\text{'}}(Y+Z^{\text{'}})$

$($f$)$ Absorption theorem: $(V^{\text{'}\text{'}}+U+W)[(W+x)+Y+U{Z}^{\text{'}}]+[(W+x)+U{Z}^{\text{'}}+]$