Show that argument form with premises
(p ^ t) --> (r v s),
q --> ( u ^ t),
u --> p,
end up with conclusion q --> r
by using rules of inference
i just want to know how would you form these arguments, and end up with
q --> r
I know how to do it with the basic ones with 1 principle say " p --> q, q, end up with p"
However, I am little confused with 2 or more principles within an arguments say " (p ^ t) --> ( r v s)"
How do i simplify something like this?
but we are no where near that as yet. for now, we know 6 statements. what can you do with them to get to (p ^ t) ?
first of all, we want to get to r, going from (r v s) to (p ^ t) makes no sense, you are going in the wrong direction. if you have r, stick with it. but it is not enough to assume you have r. you must show that you have r by assuming q. remember, we want to show q => r, so we want to start at q and get r. that is your objective. stay focused. secondly, logically you are going in the wrong direction. we have (p ^ t) => (r v s) NOT (r v s) => (p ^ t), so your line 8 does not follow by M.P. it violates the implication