## Wednesday, May 11, 2011

### If p, then q.

Today's posting (as also on April 13)  presents variations of the conditional statment -- a sentence of the form "If ___, then ___" in which mathematical theorems often are expressed. (For example, "If m is an odd integer, then m² is an odd integer.")   More generally, a conditional is a statement of the form "If p, then q" -- where p and q denote statements. Poet E. C. Jarvis plays with the language of logical statements and with the idiomatic phrase "Mind your p's and q's" in his poem, "A Simple Proposition."

A Simple Proposition     by E. C. Jarvis

If p, then mind your q's.  The p's can mind themselves.
If p and q, then mind them both.  They need it.
Never mind your r's, s's and t's.  Or, mind your p's and q's.
OR
Contrapositively to the second statement, if you don't mind
p and q, then not p or not q.
If p and not q, watch out!
If p, then q.
If q then or not p and q but rather than also.
Not r's, s's, and t's, then not mind the p's or q's and q's.
And q's if not the or p's and (not t's but s's) then if then
q's not p's or not and p's q's not and.

I found "A Simple Proposition"  in Isotope 4.2.  This journal of science and nature writing has, alas, ceased publication -- but past copies are still availailable online(A note about the poem:  The contrapositive of the conditional "If p, then q" is the statement "If q is not so, then p is not so." A statement and its contrapositive involve different wording but are "logically equivalent." The contrapositive of our exanple above about integers is "If m² is not an odd integer then m is not an odd integer."  Above, where Jarvis says "Contrapositively" he also is referring to one of DeMorgan's laws -- in particular, that the negation of the statement "p and q" is the statement "p is not so  or  q is not so."  For example, the negation of the statement "I love you and I am happy" is the statement "I do not love you or I am not happy.")