Symbolize each of the following.

1.  Everyone is a good student.
    (x)(Gx & Sx)
2.  Everyone is ambitious and works hard.
    (x)(Ax & Wx)
3.  Everyone who is a good student is ambitious and works hard.
    (x)[(Gx & Sx) -> (Ax & Wx)]
4.  There are good students.
    (Ex)(Gx & Sx)
5.  There are students who work hard.
    (Ex)(Sx & Wx)
6.  Only ambitious students do well.
    (x)[Wx -> (Ax & Sx)]
7.  There are no lazy students.
    ~(Ex)(Sx & Lx) or (x)(Sx -> ~Lx)
8.  If there are good students then all the teachers are happy.
    (Ex)(Gx & Sx) -> (x)(Tx -> Hx)
9.  Some students are lazy but everyone graduates.
    (Ex)(Sx & Lx) & (x)Gx
10.  Someone who is lazy will not be a success.
    (x)(Lx -> ~Sx)  note the need for a universal quantifier
11.  Not all students work hard although they are all ambitious.
    ~(x)(Sx -> Wx) & (x)(Sx -> Ax)   think why we should use a separate expression and repeat "Sx"
12.  There is someone who is not ambitious but only those who are ambitious will graduate.
    (Ex)~Ax & (x)(Gx -> Ax)
13.  If some do not graduate then there will be unhappy teachers.
    (Ex)(~Gx) -> (Ex)(Tx & ~Hx)
14.  All freshmen and sophomores are ambitious.
    (x)[(Fx v Sx) -> Ax]   we need a disjunction; think why
15.  Only seniors will graduate but not all seniors will graduate.
    (x)(Gx -> Sx) & ~(x)(Sx -> Gx)