$(12\%)$ Karnaugh map is not allowed in this problem.

$($a$)$ Using Boolean Algebra to simplify $(A^{\text{'}}+B)(C+D^{\text{'}})+(A^{\text{'}}+B{)}^{\text{'}}(C+D^{\text{'}}).(4\%)$

$($b$)$ Using Boolean Algebra to prove consensus theorem $xY+YZ+xZ=xY+x^{\text{'}}Z.$ You shall state the Law or Theorem used in each step $(4\%)$

$($c$)(4\%)$ Simply $G.$ You shall first write down Boolean equation of $G$ and then write down the simplified procedure and state the Laws and Theorems used.