1. (∀x)(∀y)f(x,y)=f(y,x)
2. (∀x)f(x,o)=o
-Which of the following propositions is derivable from the given premises in FF?
A) (∀x)f(x)=o
B) (∀x)f(x,x)=o
C) (∀x)f(x)=f(o)
D) (∀x)f(o,x)=o
E) (∀x)f(x,a)=f(x,x)

Question

Quizplus · Accepted Answer

Using premise 1, we know that f(o,x) = f(x,o). Using premise 2, we know that f(x,o) = o. Therefore, f(o,x) = f(x,o) = o, which means that ∀x f(o,x) = o.

1. (∀X)(∀y)f(x,y)=f(y,x) 2. (∀X)f(x,o)=o