Using Truth Tables, prove the following statement is true mark each, $4$ marks total$)$:

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

$\frac{A}{b}ar(B)$

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

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

a$)$ The truth table entry for column $\frac{?}{\text{b}\text{a}\text{r}}(A)+B=($Write your answer as an $8$ row and single column matrix $-1$ mark$)$

b$)$ The truth table entry for column $\frac{A}{b}ar(B)=($Write your answer as an $8$ row and single column matrix $-1$ mark$)$

c$)$ The truth table entry for column $\frac{?}{\text{b}\text{a}\text{r}}(A(\frac{?}{\text{b}\text{a}\text{r}}(B))+(\frac{?}{\text{b}\text{a}\text{r}}(C)))=($Write your answer as an $8$ row and single column matrix $-1$ mark$)$

d$)$ The truth table entry for column $(\frac{?}{\text{b}\text{a}\text{r}}(A)+B)C=($Write your answer as an $8$ row and single column matrix $-1$ mark$)$

CN$16-$a