Which of the following is the correct proof to show that the sum of two odd inte

Question

Which of the following is the correct proof to show that the sum of two odd integers is even? ? 5+5+10 If an integer n is even, then n # 2k where k is an integer by definition of an even integer. " k 2m +1 where m is an odd integer. 2m + 1 + 2m +1 4m + 2 2 (2m +1) An even integer is the sum of 2 odd integers. By definition, an odd integer n-2k + 1 where k is an integer. 2k +1 + 2+1 4k +2 2 (2k+1) By definition of an even integer m, m 2a where a is an integer. The sum of 2 odd integers is a multiple of 2; therefore, the sum of 2 odd integers is even. An even integer n -s 2k where k is an integer by definition of an even integer +1#2 2 is an even integer. Therefore, an even integer is the sum of 2 odd integers.

Explanation / Answer

Option 3 is the correct proof to prove that addition of two odd numbers ia an even integer.

Because in this option we have started proving the above condition by defining what an odd integer is that is by taking odd number is of form 2k+1 and eneded with proving the sum of two odd numbers is an even number by using the definition of even number.

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