Question

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.

Answer 1

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)

Answer 2

got it

thanks!!!