I am having trouble using modus ponens and all the rules of inherence. By any chance do you guys have a link that can explain these concepts in more detail. I've tried multiple books and links...and haven't found a good website that shows this types of proofs in good explanation and i am having trouble understanding it.
Suppose that statement Z says that a piece of paper will burn, Y says that a piece of paper will burn when put in a fire, and that X says that the piece of paper is in the fire.
Then Y can be written as:
X ----> Z
Modus ponens then says that if X is true and Y is true then Z must be true.
Conversely, given that Y is true and Z is false, it follows that X must be false (because if X were true Z has to be true). So the statement:
X ----> Z
is equivalent to
Not(Z) ---> Not(X)
got it
thanks!!!
I can definitely help you with that! Modus ponens is a valid rule of inference, and it is commonly used in deductive reasoning. It allows you to draw a conclusion from two premises: the first premise asserts a conditional statement, and the second premise affirms the antecedent of that conditional statement.
To understand modus ponens and other rules of inference more thoroughly, I recommend checking out websites and resources that focus on logic and proof theory. Here are a few suggestions to get you started:
1. Stanford Encyclopedia of Philosophy: You can find detailed explanations and examples of various logical rules, including modus ponens and other rules of inference. Visit their website (plato.stanford.edu) and search for logic-related articles.
2. MathIsFun: This website provides a comprehensive guide to different logical rules, including modus ponens and other derivations. You can find easy-to-understand explanations along with numerous examples. Visit their website (mathsisfun.com) and search for "rules of inference" or "proofs in logic."
3. YouTube tutorials: Many educational channels offer video explanations of logic concepts and rules of inference. Search for channels like "MathDoctorBob" or "Michael Ewins" as they have videos on this topic. Watching visual demonstrations can often enhance your understanding.
4. University course websites: Check the websites of universities that offer courses in logic or formal methods. Some universities provide online resources, lecture slides, and problem sets that cover modus ponens and other rules of inference. Look for courses in philosophy, mathematics, or computer science departments.
Remember, it's important to practice and work through examples to solidify your understanding. Try to solve problems and proofs using modus ponens and other rules of inference on your own. This active engagement will greatly contribute to your comprehension and mastering of these concepts.