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If n 1 n 2 , . . . . . . . . . . . . . . . . . n p are p positive integers, whose sum is an even number, then the number of odd integers among them is odd.

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

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
8 years ago
Consider N = n1 + n2 + n3 + . . . . . . . . +np 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.

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