a$)$ Use the predicate specifications:

$b(x,Y)$:$x$ scares $Y$

$c(x)$:$xis$ a cat

$d(x,Y)$:$x$ chases $Y$

and the constant symbols:

D: dog

M: mouse

B: bird

to translate the following natural language statement into predicate logic:

Some cat scared a dog which chased a mouse but was frightened by a bird.

b$)$ Consider the predicate logic formula:

AAx$(EEy(P(x,y{)}^{{?}^{?}}Q(y))(EEyR(y,x{)}^{{?}^{?}}$AAzS$(z,y))).$

Identify a variable which has both free and bound occurrences in this formula. Mark the two occurrences in the formula, the one where it is bound and the other where it is free. If there is no such variable for any part of the question, write no such variable exists.