Modus Tollens is like a detective who solves mysteries by checking if something is not true to figure out what else isn’t true.
Imagine you have a toy robot that sings when it has batteries. If the robot sings, we know it has batteries. But if the robot does not sing, then we can say for sure it does not have batteries. That's Modus Tollens in action, going from “no singing” to “no batteries.”
How It Works
Let’s break it down with a rule:
- If A happens, then B happens.
- If B does not happen, then A does not happen.
In our robot example:
- A = the robot has batteries
- B = the robot sings
So, if the robot doesn’t sing (not B), we can say it doesn't have batteries (not A). It’s like a puzzle piece, when one part is missing, you know something else is missing too.
You use this every day. If your favorite ice cream is gone and the bowl is empty, you know someone ate it. That's Modus Tollens in real life!
Examples
- If it rains, the ground gets wet. The ground is not wet, so it did not rain.
- If a cat is hungry, it meows. The cat is quiet, so it is not hungry.
- If you study, you pass the test. You failed the test, so you didn’t study.
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See also
- How Does 1 Arguments Work?
- How do we express logic?
- Explainer: What Is an Algorithm?
- How Does [Discrete Mathematics] Direct Proofs Examples Work?
- How Does Computer Science Basics: Algorithms Work?