The model

$\frac{dx}{dt}=4(x-xy-\frac{x^2}{4}),$

$\frac{dy}{dt}=2(y^2-\frac{y}{2}),$

describes two interacting species, $x$ and $y.$ Which of the following statements are TRUE and which are FALSE? Justify your answers! First, draw a phase diagram to answer the below questions. Also, note that phase diagrams drawn by an automated plotter will be awarded zero.

$(3\mathrm{.}1)$ This is a Predator$-$Prey system, where x is the predator and y is the prey.

$(3\mathrm{.}2)$ Species $y$ can survive without species $x.$

$(3\mathrm{.}3)$ Species $x$ can survive without species $y.$

$(3\mathrm{.}4)$ The two species are competing for the same resources.

$(3\mathrm{.}5)$ If the initial populations are large enough, both populations can grow without bound.

$(3\mathrm{.}6)$ Both populations will always die out.