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goldenfox [79]
3 years ago
14

Use a proof by contradiction to prove that the sum of two odd integers is even.

Mathematics
1 answer:
Troyanec [42]3 years ago
4 0

Answer:

Step-by-step explanation:

to prove that the sum of two odd integers is even.

Let a and b be two odd integers.

If possible assume that

a+b = 2m, i.e. sum is a product of 2, hence even.

Since a is odd,

a=2k+1\\ for some integer k.

Subtract a from a+b to get

b = 2m+1-(2k+1)\\= 2m-2k\\=2(m-k)\\=2l

i.e. b is a multiple of some integer l by 2

i.e. b is even.

This contradicts our assumption that both a and b are odd

Hence proved that the sum of two odd integers is even.

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