Proving and Disproving Statements in Logic

To prove an "if-then" statement, mathematicians start by pretending the "if" part is already

true. Seriously. It's a technique called "assuming the hypothesis."

You just accept the first part as fact and then use pure logic to show the "then" part

absolutely has to follow. It’s like building an unbreakable logical bridge from your

starting point to your conclusion. But if you want to disprove a statement like "all birds

can fly"? You don't need a bridge. You just need to find one single

penguin. One counter-example is all it takes to bring the whole theory crashing

down.