TOPICS
Search

Direct Proof


A direct proof establishes a conditional proposition P=>Q by assuming the hypothesis P and deducing the conclusion Q through definitions, previously established results, and valid rules of inference. Unlike an indirect proof, it does not begin by assuming the negation of the desired conclusion.

For example, to prove directly that the sum of two even integers is even, write a=2m and b=2n. Then a+b=2(m+n), which is even by definition.


See also

Indirect Proof, Proof, Proof by Contradiction, Proposition

Explore with Wolfram|Alpha

References

Velleman, D. J. How to Prove It: A Structured Approach, 3rd ed. Cambridge, England: Cambridge University Press, 2019.

Cite this as:

Weisstein, Eric W. "Direct Proof." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DirectProof.html

Subject classifications