- #1
njama
- 216
- 1
"A direct proof is a proof in which the truth of the premises of a theorem are shown to directly imply the truth of the theorem's conclusion."
Here are the premises:
(P -> R) ^ (Q -> S) ^ (~P) ^ (P v Q)
and the conclusion:
(S v R) ^ (~P)
Now what I do not understand why we are using expressions that are implications are not equivalency?
Let me start the prrof.
(1) ~P premise
(2) P v Q premise
(3) From discjunctive simplification we got:
(P v Q) ^ (~P) -> Q
(4) (Q->S) premise
(5) From detachment i.e (Q->S) ^ Q -> S
(6) P -> R premise
(7) from (6) ~P v R
And I didn't come up with the conclusion? What is the problem with this direct proof?
Shouldn't I use equivalent expressions and not implications?
Please help
Here are the premises:
(P -> R) ^ (Q -> S) ^ (~P) ^ (P v Q)
and the conclusion:
(S v R) ^ (~P)
Now what I do not understand why we are using expressions that are implications are not equivalency?
Let me start the prrof.
(1) ~P premise
(2) P v Q premise
(3) From discjunctive simplification we got:
(P v Q) ^ (~P) -> Q
(4) (Q->S) premise
(5) From detachment i.e (Q->S) ^ Q -> S
(6) P -> R premise
(7) from (6) ~P v R
And I didn't come up with the conclusion? What is the problem with this direct proof?
Shouldn't I use equivalent expressions and not implications?
Please help