For the following statements the universe comprises all nonzero integers. Determine the truth value of each statement.
(a) ∃x ∃y [xy = 1]
(b) ∃x ∀y [xy = 1]
(c) ∀x ∃y [xy = 1]
(d) ∃x ∃y [(2x + y = 5) ∧ (x - 3y = - 8)]
(e) ∃x ∃y [(3x - y = 1) ∧ (2x + 4y = 3)]