Question #142685
Statement: “The product of an even number and any other number is even.”
Using direct proof method.
1
Expert's answer
2020-11-08T18:37:41-0500

Suppose n is even integer. Then by the definition of even numbers, n = 2k for some integer k.

Suppose m is an integer.

Then by substitution we have mn=m(2k)=2(mk)=2qm\cdot n=m(2k)=2(mk)=2q for some integer q=mkq=mk. Therefore by the definition of even numbers the product mnm\cdot n is an even number.

 This completes the proof.

Therefore, the product of an even number and any other number is even.



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