Q$3(50$pts$)$: Prove both of the following Boolean equations using the axioms and theorems of Boolean algebra. Write down explicitly which theorems are used in each step of the derivation.

a$)A^{\text{'}}B(CD+D^{\text{'}})+A^{\text{'}}B{C}^{\text{'}}D+AB=B$

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