1. (∀x)(∀y){Pf(x,y) ⊃ [Pf(x,x) • Pf(y,y)]}
2. a=f(d,b)
3. Pa
-Which of the following propositions is an immediate (one-step) consequence in FF of the given premises?
A) a=f(b,d)
B) a=f(b,b)
C) Pf(d,b)
D) (∀y){Pf(x) ⊃ [Pf(x) • Pf(y)]}
E) (∀y){Pf(x,x) ⊃ [Pf(x,x) • Pf(x,x)]}

Question

Quizplus · Accepted Answer

Given the premises, the most direct consequence is C) Pf(d,b), as it directly follows from premise 2 (a=f(d,b)) and premise 3 (Pa) by substituting 'a' with 'f(d,b)' in the predicate Pf, thus applying the given information without additional assumptions or transformations.

1. (∀X)(∀y){Pf(x,y) ⊃ [Pf(x,x) • Pf(y,y)]}