Everyone fears someone (or other).
A) (x)(y)[(Px • Py) ⊃ Fxy]
B) (x)(∃y)[(Px • Py) ⊃ Fxy]
C) (∃x)(y)[(Px • Py) • Fxy]
D) (x)(∃y)[(Px • Py) • Fxy]
E) (∃x)(∃y)[(Px • Py) • Fxy]

Question

Quizplus · Accepted Answer

Choice D correctly captures the idea that there exists someone who is feared by someone else. The universal quantifier over x ensures that every person fears someone, and the existential quantifier over y allows for the possibility that someone is feared without necessarily fearing someone else. Choices A, B, and C are too strong or too weak in their quantification, and choice E goes too far by asserting that every person both fears and is feared by someone else.

Everyone Fears Someone (Or Other)