Consider a signature with constants a, b; unary function symbols f, g; unary predicate symbols p, q; and a binary predicate symbol r. We consider a structure with a universe U = {0, 1, 2, 3} and an interpretation I that maps the symbols above as follows: I(a) = 0 I(b) = 1 I(f)(x) = 1 if x = 1, and I(f)(x) = 2 otherwise I(g)(x) = (x + 2) % 4 I(p)(x) = t if x = 0, and I(p)(x) = f otherwise I(q)(x) = t if x >= 2, and I(q)(x) = f otherwise I(r)(x, y) = t if x < y, and I(r)(x, y) = f otherwise Which of the following first-order sentences are satisfied under this structure?

Consider a signature with constants a, b; unary function symbols f, g; unary p...

Consider a signature with constants a, b; unary function symbols f, g; unary predicate symbols p, q; and a binary predicate symbol r.

We consider a structure with a universe U = {0, 1, 2, 3} and an interpretation I that maps the symbols above as follows:

Which of the following first-order sentences are satisfied under this structure?