# Talk:Constructive dilemma

WikiProject Philosophy (Rated Stub-class)
This article is within the scope of WikiProject Philosophy, a collaborative effort to improve the coverage of content related to philosophy on Wikipedia. If you would like to support the project, please visit the project page, where you can get more details on how you can help, and where you can join the general discussion about philosophy content on Wikipedia.
Stub  This article has been rated as Stub-Class on the project's quality scale.

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, ${\displaystyle p\lor r}$ 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)