What are direct proofs?

A direct proof is like showing your friend how to build a tower by stacking blocks, step by step, clearly.

Imagine you want to prove that if it's raining, the ground gets wet. A direct proof means you start with "it's raining" and then show exactly how that leads to "the ground gets wet." No secrets, no tricks, just real, simple steps.

Like Building a Sandwich

Think of a direct proof like making a sandwich. You know the recipe: bread, peanut butter, jelly. If you start with bread, then add peanut butter, then jelly, and finally the other piece of bread, that’s how you make a sandwich, step by step, just like in a direct proof.

You don’t say “magic happens,” or “it becomes a sandwich out of nowhere.” You show exactly what you did to get there. That's how a direct proof works, it shows the clear path from what we know to what we want to prove.

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Examples

  1. Proving that if it rains, the ground gets wet by saying 'it rained and the ground is wet.'
  2. If you eat a lot of candy, then you will get a stomachache. You ate a lot of candy, so you have a stomachache.
  3. If you study for an exam, you pass it. You studied, so you passed.

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Categories: Math · proofs· logic· mathematics