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What can you say about the sum of an even integer and an even integer use inductive reasoning to form a conjecture then use deductive reasoning to show that the conjecture is true?
Wiki User
∙ 11y ago
Conjecture: the sum of two even integers is always an even integer.
Suppose M and N are two even integers.
M is even and so it is divisible by 2 without remainder. That is to say, there is some integer X, such that M = 2X.
Similarly, N = 2Y for some Y.
Then M + N = 2X + 2Y
=2*(X + Y) due to the distributive property of multiplication over addition of integers.
And, by the closure of the set of integers under addition, X+Y is an integer.
Therefore, M + N is equal to 2 times an integer and therefore it is an even integer.
Wiki User
∙ 9y ago
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