From the course: Programming Foundations: Discrete Mathematics

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Solution: Write a proof

Solution: Write a proof

From the course: Programming Foundations: Discrete Mathematics

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Solution: Write a proof

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- [Voiceover] How did you make out with the proof challenges? I'd like to go over my solution. The first proof said if three x plus five is an odd number, then x has to be an even integer. So for this example, we let x equal two k which our definition of even numbers. We substitute two k in for x and we get three times two k plus five which is six k plus five. Now here's the tricky part. Remember five is the same thing as four plus one. So I'm gonna replace five and I get six k plus four plus one. Now I can factor it two out of the six k plus four and now I get two times a quantity three k plus two plus one. And remember, integers are close under addition. So that means three k plus two is an integer and two times an integer plus one is an odd number. So the original proof holds. The next proof says, "If the square of an integer x is even, "then x is even." This one might be easier to approach using the contrapositive. Remember the contrapositive is logically equivalent to the…

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