Whoever rides horses is adventurous.
A) (x){Px • (∃y)[(Hy • Rxy) ⊃ Ax]}
B) (x){[Px • (∃y)[(Hy • Rxy)] ⊃ Ax}
C) (x){[Px • (y)[(Hy • Rxy)] ⊃ Ax}
D) (∃x)(Px • Rxh) ⊃ (∃y)Ay
E) (x)Px ⊃ (∃y)[(Hy • Rxy) ⊃ Ax]

Question

Quizplus · Accepted Answer

Choice B correctly captures the statement by stating that whoever rides horses (there exists a y such that the person x and the horse y have a riding relation) and is adventurous (they have the property of being adventurous) implies that person x has the property of being adventurous as well. Choice A incorrectly introduces a universal quantifier for y which means that every horse has a riding relation with person x which is not true. Choice C wrongly introduces a universal quantifier inside the implication which means that every person x has a riding relation with every horse y, regardless of the person's adventurous nature. Choice D introduces existential quantifiers and a new variable h which is not given in the statement. It also wrongly implies that the existence of one person who rides horses (with horse h) implies that there exists another person who is adventurous, regardless of their relation to horse h. Choice E wrongly implies that every person who exists has a relation with a horse (it is not given in the statement) and also that only if they have a riding relation with a horse that is adventurous will they themselves be adventurous.

Whoever Rides Horses Is Adventurous