1.

a) xy Lxy

b) x yLxy

c)  ∃ xy ~Lxy

d) xLxg

e) xyLyx

f) ~xy Lyx

g) xy ~Lxy

2.

a) x( Sx y ( By Hxy ))

b) x( Sx y ( By ~ Hxy ))

c) x( Sx y ( By Hxy ))

d) ~x( Sx y ( Bx Hxy ))

e) x( Bx y ( Sy Hxy) ))

3.

a) x( Bx ~ Ex )

b) x( ( Bx Ex ) Gx )

c) x( Bx ~ Gx )

d) No.

4.

a) x( ~Gx ~ Fx )

b) x( Zx Mx)

c) x( Mx Fx)

d) x( Zx Gx )

e) Yes. For an arbitray animal x if Zx, then Mx by b). Then by c) Fx holds for that x. Hence from a) by modus tollens Gx holds.