Task $3$: The above Boolean expression can be simplified as given below.

Example $2$: Simplify the following expression:

$Q\frac{?}{b}=ar(A)*B+A*B\frac{*}{b}ar(C)+A*B+C$

There is a common factor, $A.B,$ in the second and third terms. Extracting it gives:

$Q\frac{?}{b}=ar(A)*B+A*B*(\frac{?}{\text{b}\text{a}\text{r}}(C)+1)+C$

In doing so$,$ we used identity $1$ in reverse, replacing $A.B$ with $A.B\mathrm{.}1.$

Using identity $5,$ the term $(\frac{?}{\text{b}\text{a}\text{r}}(C)+1)=1,$ so the expression becomes:

$Q\frac{?}{b}=ar(A)*B+A*B*1+C$

Using the first identity then reduces the expression to:

$Q\frac{?}{b}=ar(A)*B+A*B+C$

There is a common factor, $B,$ in the first two terms. Extracting it gives:

$Q=B*(\frac{?}{\text{b}\text{a}\text{r}}(A)+A)+C$

Using identity $8,$ the expression reduces to:

$Q=B\mathrm{.}1+C$

With identity $1,$ the final expression is:

$Q=B+C$

a$-$ Construct the logic circuit and truth table for the simplified expression $Q=B+C$

Provide screenshots for each combination of inputs. $($All Screenshots should include your full name in the middle of the circuit$)$

$\backslash$table$[[$A$,$B$,$C$,$Q$],[0,0,0,],[0,0,1,],[0,1,0,],[0,1,1,],[1,0,0,],[1,0,1,],[1,1,0,],[1,1,1,]]$

b$-$ Write your observation based on the output of Task$1$ and Task$2$