What is the truth table for the following logic operation? Prove that by building the logic circuit. $($A$,$ B$,$ C and D are inputs$)$

i$)$ Output $=((A^{\text{'}}+B)o+C^{\text{'}}).$ B

ii$)$ Output $=(A^{\text{'}}{B}^{\text{'}}+C)o+(D+BC)$

iii$)$ Output$1=(((A^{\text{'}}o+B)+C.D),BA{)}^{\text{'}}$

Output$2=(A+B)*(D^{\text{'}}+C^{\text{'}})$