Q$3.$ Determine the function at the OUT terminal implemented by transmission gate logic shown

below.

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

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

$($c$)A^{\text{'}}{B}^{\text{'}}+A^{\text{'}}BC+AB{C}^{\text{'}}$

$($d$)A^{\text{'}}{B}^{\text{'}}+A^{\text{'}}BC+A{B}^{\text{'}}+AB{C}^{\text{'}}$

$($e$)AB+A^{\text{'}}BC+AB{C}^{\text{'}}$