Relationship between adders

$(10$ pts$)$

Notice that there is a relationship between the half adder and full adder. Use the Boolean equations in $1[a],[$b$]$ and $2[a],[b]$ to extract the relationship between both circuits. In other words, write the Boolean function of the full adder in terms of the half adder expressions $($review class slides where it was explained in detail$).$

You can use $()HA,$ and Cout ${?}_{HA}$ to represent the half$-$adder sum and carry outputs. While the Sum $F_{FA},$ and Cout.. to renresent the full adder sum and carry$-$out bits.