Conditional proof

Conditional proof is like a special way of doing math problems. It helps you to figure out if something is true or not by making up imaginary things called "assumptions" and seeing what would happen if they were true.

Imagine you are trying to solve a math problem that says "If X is greater than 5, then Y is less than 10." You want to prove whether this statement is true or not. Here's how you can use a conditional proof:

First, you make an assumption that X is greater than 5. This means you pretend that X is a big number, like 7 or 9. Then, based on that assumption, you try to figure out whether Y is less than 10. You might use some basic math rules, like subtraction or division, to help you.

Next, you treat your assumption like it's a fact, even though it might not be true in real life. This means you can use it to help you make new statements that are also true. For example, you might say "If X is greater than 5, then X minus 2 is greater than 3." This is true because 7 minus 2 is 5, which is greater than 3.

Finally, you use your assumption and any other true statements you've figured out to see if the original statement is true or not. In this case, if you've proven that "If X is greater than 5, then X minus 2 is greater than 3," and you know that 7 minus 2 is 5, which is greater than 3, then you can conclude that "If X is greater than 5, then Y is less than 10" is true.

Overall, conditional proof is a way to use imaginary assumptions to help you figure out if something is true or not. It's like building a puzzle or following a map to get to the answer you're looking for.