premise is -p
-r -> p therefore -r, modus ponens
is this assumption correct?
this is not using modus ponens, and it's not true anyway. Remember, $\displaystyle \neg R \implies P$ is the same as saying $\displaystyle \neg P \implies R$. Since $\displaystyle \neg P$ is true, $\displaystyle R$ follows by modus ponens, not $\displaystyle \neg R$
thanks
how about
premise -q
-p or q, therefore p, disjunctive syllogism
if q is false then p must be true, otherwise the whole condition is false??
or is it,
if -q(i.e. q is false)
then -p must be true for -p or q.
??
so
premise -q
-p or q, therefore -p, disjunctive syllogism
??
thanks for the help
the question I am working on is:
-r --> p, (-p) or q, -s -->(-p)and (-r), (-p) and r --> (-s) or t, -q, therefore t.
So far I have
1: -p, -p or q therefore -p conjunctive syllogism
2: -p, -r --> p therefore r modus ponens
3: -p, r, therefore -p and r conjunctive addition
(the next 2 lines I am unsure of)
4: -p and r, -s --> (-p) and(-r) /*-p is true from 1. but r is true from 2, so -r is not true. therefore (-p) and(-r) is not true so - (-p) and(-r) = -(p or r) demorgans.??? I don't know where to go with this? */
therefore s, because -s --> (-p) and(-r) is false.
5: (-p) and r (from 3), -s is false, (-s) or t therefore t disjunctive syllogism
am I close to showing the argument is valid??
thanks for any input and help
so -s --> (-p) and(-r)