Apparently this question is hard

Let $\displaystyle Q(a,b)$ be a property which involves a and b. Let $\displaystyle P(c)$ be a property which involves c. For this problem, the domain will be the reals. For each of the following below, find properties $\displaystyle P(c)$ and $\displaystyle Q(a,b)$ such that:

a.) $\displaystyle (\forall x)(\forall z)[Q(x,z) \implies Q(z,x)]$ is true.

b.) $\displaystyle (\forall x)(\forall z)[Q(x,z) \implies Q(z,x)]$ is false.

c.) $\displaystyle (\forall x)[P(x) \implies (\exists z) Q(x,z)]$ is true.

d.) $\displaystyle (\forall x)[P(x) \implies (\exists z) Q(x,z)]$ is false.