Talk:Constructive dilemma

Thanks to numerous named and anonymous editors on the other symbolic logic articles, I borrowed extensively from article layouts. Zenosparadox 15:27, 23 Dec 2004 (UTC)

Not exclusive or
The final statements here, "Because one cannot have P&R, one cannot have both Q&S. In this example, the situation in which Ronald Reagan and Jimmy Carter are both presidents produces a logical contradiction.", seem wrong. Of course you can't have two presidents at once, but in symbolic logic, $$ p \lor r $$ indicates the inclusive or, p or r or both. --Jwwalker 16:23, 15 May 2005 (UTC)

Does this go both ways?
From (A -> B) + (C -> D)

Can you derive (A v C) -> (B v D) ?

You can if you are given premises of ~B and ~C. Proof is

1) (A -> B) + (C -> D)

2) ~B

3) ~D

4) (A -> B)          /1, Simplification

5) (C -> D)          /1, Simplification

6) ~A                /2, 4, Modus Tollens

7) ~C                /3, 5, Modus Tollens

8) ~A + ~C           /6, 7, Conjunction

9) ~(A v C)          /8, Rule of equivalences (I think distribution)

10) ~(A v C) v (B v D)/9, Addition

11) (A v C) -> (B v D)/10, Rule of equivalence (I forget which one)

Hope someone can expound on this --PrinceXantar 12:05, 24 March 2010 (UTC)