THE PROPOSITION CAN BE FALSE

72. The proposition can be false. Let N denote the set of persons James James, Terry James, and

Lee James; let the domain of discourse be N × N ; and let P (x, y) be the statement “x’s first

name is the same as y’s last name.” Then ∃x∀yP (x, y) is true, but ∀x∃yP (x, y) is false.