Write the truth table and equation for the following circuit diagram. Do not do any simplification on

the equation when written for your answer. $(5$ points$)$

The following Boolean Properties are to be used and referenced by name for each$/$every step to receive full

credit when you "show your work" during the remaining problems in this homework.

Boolean Algebra Property

$a*(b+c)=a*b+a*c$

$a+(b*c)=(a+b)*(a+c)$

$a*b=b*a$

$a+b=b+a$

$(a*b)*c=a*(b*c)$

$(a+b)+c=a+(b+c)$

$a^{*}{a}^{\text{'}}=0$

$a+a^{\text{'}}=1$

$a*1=a$

$a+0=a$

$a*0=0$

$a+1=1$

$a*a=a$

$a+a=a$

$(a^{\text{'}}{)}^{\text{'}}=a$

$(a^{-}*b{)}^{\text{'}}=(a^{\text{'}}+b^{\text{'}})$

$(a+b{)}^{\text{'}}=(a^{\text{'}}*b^{\text{'}})$

Name

Distributive $($AND$)$

Distributive $($OR$)$

Commutative

Associative

Complement $($AND$)$

Complement $($OR$)$

Identity $($AND$)$

Identity $($OR$)$

Null elements

Idempotent

Involution

DeMorgan's $($AND$)$

DeMorgan's $($OR$)$