From the course: Programming Foundations: Discrete Mathematics

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Evaluate conditional proofs

Evaluate conditional proofs

From the course: Programming Foundations: Discrete Mathematics

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Evaluate conditional proofs

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- [Voiceover] When evaluating conditional proofs it's important to first review the definitions in previously proven theorems related to number theory. An integer n is even if, and only if n equals twice some integer written as n equals two k. An integer n is odd if, and only if, n equals twice some integer plus one, written as n equals two k plus one. An integer n is prime if, and only if, n is greater than one and for all positive integers r and s, if n is equal to r times s, then either r equals one or s equals one. In other words, n is prime as long as n is only divisible by one and itself. An integer n is called a perfect square if, and only if, n equals k squared for some integer k. A real number r is considered rational if, and only if, it can be expressed as a quotient of two integers with a nonzero denominator. A previously proven theorem says that the sum of any two rational numbers is rational. And finally, it's important to know that integers are closed under addition…

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