Deduction theorem

Alright kiddo, so let me explain the concept of deduction theorem to you in a really simple way.

Have you ever played a guessing game where someone asks you a question, and you have to give them an answer based on the clues they give you? That's kind of like what deduction theorem is, except it's used in math and logic.

Deduction theorem is a rule that mathematicians and logicians use to help them figure out if certain statements or equations are true or not. It basically allows them to "deduce" or figure out something new based on what they already know.

Here's an example: let's say we know that "if it's raining outside, then the ground is wet." We also know that "it's raining outside." Based on those two statements, we can "deduce" or figure out that "the ground is wet."

The way we do this is by using the deduction theorem, which says that if we have a certain set of statements (in this case, "if it's raining outside, then the ground is wet" and "it's raining outside"), and if we introduce a new statement that follows logically from those previous statements (in this case, "the ground is wet"), then we can say that the new statement is also true.

So in essence, deduction theorem allows us to use logic to figure out new things based on what we already know. It's like a puzzle or a game, but with numbers and equations instead of words and pictures.

Does that make sense, kiddo? Let me know if you have any questions!