Module 8 Essay: Which do you prefer Direct or Indirect Proof? Why?
Answers
Suppose you and your friend Rachel are going to an art festival. When you get there, you are the only ones there. Rachel looks at you and says, ''If the art festival was today, there would be hundreds of people here, so it can't be today.''
You take out your tickets, look at the date and say, ''The date on the tickets is for tomorrow, so the art festival is not today.''
Notice that both you and Rachel came to the same conclusion, but you got to that conclusion in different ways. As it turns out, your argument is an example of a direct proof, and Rachel's argument is an example of an indirect proof.
A direct proof assumes that the hypothesis of a conjecture is true, and then uses a series of logical deductions to prove that the conclusion of the conjecture is true.
An indirect proof relies on a contradiction to prove a given conjecture by assuming the conjecture is not true, and then running into a contradiction proving that the conjecture must be true.