Give fluent english readings for the following sentences of ple using the given symbolization key. ud: the set of positive integers lxy: x is less than y gxy: x is greater than y ex: x is even ox: x is odd px: x is prime f(x, y): the product of x and y t: 2 f: 5 n: 9 a. (∀x)(∃y)lxy *b. (∃x)(∀y)(∼ x y ⊃ lxy) c. (∃x)(∀y) ∼ lyx *d. ∼ (∃x)(ex & lxt) e. (pt & et) & (∀x)[(px & ex) ⊃ x t] *f. ∼ (∃x)(∃y)[(px & py) & pf(x, y)] g. (∀y)(∀z)[(oy & oz) ⊃ of(y, z)] *h. (∀y)(∀z)[(ey & ez) ⊃ ef(z, y)] i. (∀y)(∀z)[(ey ∨ ez) ⊃ ef(y, z)] *j. (∀x)[ex ⊃ (∃y)(oy & gxy)] & ∼ (∀x)[ox ⊃ (∃y)(ey & gxy)] k. (∃x)[[px & (gxf & lxn)] & (∀y)([py & (gyf & lyn)] ⊃ y x)]