If n₁ n₂, . . . . . . . . . . . . . . . . . n_p are p positive integers, whose sum is an even number, then the number of odd integers among them is odd.

Consider N = n₁ + n₂ + n₃ + . . . . . . . . +n_p where N is an event number. Let k numbers among these p numbers be odd, then p – k are even numbers. Now sum of (p – k) even numbers is even and for N to be an even number , sum of k odd numbers must be even which is possible only when k is even.

∴ The given statement is false.