Are ~(pv~q) and ~p^q logically equivalent? Explain
2007-02-17 15:25:09 · 5 answers · asked by fouche-james 1 in Science & Mathematics ➔ Alternative ➔ Parapsychology
Yes.
Mytraver, the second one is "not p AND q".
Syntactic explanation: you can obtain one from the other one with the deMorgan rules.
Semantic explanation: in a truth table, they have the same truth values. Or: they have the same truth value in any possible world.
(no more parapsychology... please... this would crash down any logician's self-esteem :) Logical questions belong either to "philosphy", or to "mathematics".)
2007-02-17 23:42:24 · answer #1 · answered by jlb 2 · 3⤊ 0⤋
So you are asking if
not (P or Not q) is the same as Not p or q.
No they are not the same - In the first case we have something which is neither P or Not q
In the Second case we have something which is Not P AND q.
In the first case the subject COULD be q, in the second it could not becasue it would have to be BOTH ~p AND ~q to satisfy the obverse of the statement (You can usually tell if your going the right way with symbolic logic if the reverse of your statement satisfies the opposing conditions). TO observe take the converse case - is something P or Not q (pv~q) If it is P then it is not q, therefore something which is ~(pv~q) is q as it is not p.
The second statement ~p^q is cumulative - in order to be attributed to this statement, a thing must be BOTH not p and not q (~p) and (~q), since the statement tells us that is is NOT p and q, thus illiminating the possibility that something is BOTH P AND q, and is therefor neither.
Since the first statement allows for the possibility of being q and the second does not, they are not logically equivalent.
Hope that helps!
2007-02-18 00:03:31 · answer #2 · answered by mytraver 3 · 0⤊ 0⤋
You really like us doing your logic homework for you don't you....the best thing to do is go to class, listen, ask questions for clarification and then......oh my god......do your own homework!!!!!!!!!
It's a hard subject but it can be done if you actually try.
2007-02-19 09:46:45 · answer #3 · answered by Yogini 6 · 0⤊ 0⤋
Again I am confused. What does this have to do with parapsychology?
BB
2007-02-21 14:34:24 · answer #4 · answered by Anonymous · 0⤊ 0⤋
venn-diagram indicates "yes"
(Venn-diagram is the *easiest* way to see it, but I don't kow what level of rigor you seek)
2007-02-21 04:06:50 · answer #5 · answered by atheistforthebirthofjesus 6 · 0⤊ 0⤋