The logic circuit shown in the diagram directly implements which of the Boolean expressions given below?

$((xy)+(x+y{)}^{\text{'}})$

$((x+y{)}^{\text{'}}(x{y}^{\text{'}}){)}^{\text{'}}$

$((xy{)}^{\text{'}}(x+y^{\text{'}}){)}^{\text{'}}$

$((x{y}^{\text{'}})+(xy{)}^{\text{'}})$