THE PROPOSITION CAN BE TRUE

81. The proposition can be true. 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 different from y’s last name.” Then ∀x∃yP (x, y) is false, but ∃x∀yP (x, y) is true.