Consider the open statement
p(x, y): y - x = y + x2
where the universe for each of the variables x, y comprises all integers. Determine the truth value for each of the following statements.
(a) p(0, 0)
(b) p(1, 1)
(c) p(0, 1)
(d) ∀y p(0, y)
(e) ∃y p(1, y)
(f) ∀x ∃y p(x, y)
(g) ∃y ∀x p(x, y)
(h) ∀y ∃x p(x, y)