please answer a), b), c), and d) of problem 4

Problem 4 [20 points] Consider predicate logic formulas over the set of variables V={x,y,z}, the set of function symbols F={g}, and the set of predicate symbols P={P,Q}. Suppose that we have a model M=(DM,FM,PM) where DM={1,2,3,4}FM={gM}PM={PM,QM} gM and PM are defined as follows and QM is defined such that for all d1 and d2DM, QM(d1,d2)={true,if(d1=1d2=2)(d1=2d2=4)(d1=3d2=2)false,otherwise For each of the formulas f1,f2,f3, and f4 in the following four questions, determine whether M=f1 or M=fi, that is, whether it holds in the model. Write "holds" as the answer if the formula holds and write "does not hold" otherwise. Also, justify your answer briefly and precisely. (a) (5 points) f1:x((yQ(y,x))P(x)) (b) (5 points) f2:y(Q(g(y),y)Q(y,y)) (c) (5 points) f3:z(P(z)P(g(z))) (d) (5 points) f4:xy(P(x)Q(x,y)) i.e., forall x exists y(P(x) iff Q(x,y))