How can I figure out

$103.$ Derive the output expression $x,$ of the following logic circuit. Simplify it$,$ with respect to the minimal number of gates and minimal number of inputs to the gates.

The "optimal" simplified binary output is:

$($a$)A\frac{+}{b}ar(B)\frac{+}{b}ar(C)$

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

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

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

$($e$)$ None of the above

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