I have the following:
B(x) stands for "x is a baker",
F(x) stands for "x is a farmer",
K(x,y) stands for "x knows y".
Ax: for all x
Ex: there exists an x
(a) Express "Everybody knows a farmer" in terms of predicate logic.
For this I have:
Ax(Ey (F(y) -> K(x,y))
Which I believe translates to "For all X, there exists a farmer Y, such that X knows a Y". Which in turn implies that everybody knows a farmer.
Now, the second question is:
(b) "Everybody knows someone who knows a farmer"
This one confuses me, as the same relation is involved twice.
So far, I have:
Ax(Ey K(x,y) -> (K(y,z) && Ez(F(z))
But this does not seem right. How do I approach this question?