Symbolize the following sentences in pl, using quantifiers wherever appropri- ate, using the following symbolization key:
ud: the set of seniors at dartmouth college .
gy: y will graduate.
jy: y will get a job.
ay: y join the army ly y will become a longshoreman.
mxy: x wl make more money than y.
b: bob.
c: carol.
d: david.
e: emily.
a. all of those who graduate will get jobs.
b. if david will graduate, all seniors will graduate.
c. if at least one senior graduates, they will all graduate.
d. everyone who doesn't graduate will join the army.
e. if anyone joins the army both carol and david will.
f. everyone will graduate or no one will graduate.
g. each senior will either graduate or not graduate.
h. if anyone who graduates becomes a longshoreman emily will become a long shoreman.
i. everyone who becomes a longshoreman will make more money than will eve- ryone who does not.
j. each senior will join the army if and only if he or she does not graduate.