Re: Logic statements (was RE: What is understanding?)

[Gary Karshner <karshner@STMARYTX.EDU>]

Cary,
        I think it is time to put my foot in my mouth, and state what I remember
from mathematical logic a long long time ago:
        Conditional             Inverse

        Converse                Contrapositive

If the conditional is true then so is the contrapositive, it is the inverse
of the converse or the converse of the inverse!

If the inverse is true then so is the converse!

But the conditional does not imply anything about the truth or falsity of
the either the inverse or converse.

All of these conditions are valid for two level logic, i.e. one where
statements  are either true or false. In Boolean algebra it evolves into De
Morgan's theorem.
        I think I have stated more then I know, so I will shut up. Who says we
have to understand it to teach it?

Gary

> The complication with this particular statement of logic is that it begins
> with negatives.  I will try to fit it into the pattern suggested by K.
>
> (Rephrased): If I cannot create it, I do not understand it.
> :  If I do not understand it, I cannot create it.
> :  If I do understand it, I can create it.
> :  If I can create it, I do understand it.
>
> > Just for clarification, If I recall correctly:
> >
> > Conditional:  If  A then B
> > Converse:  If B then A
> > Inverse:  IF  NOT A then NOT B
> > Contrapositive:  IF NOT B then NOT A
> >
> > If the conditional and converse are both true then  a biconditional.
What is a biconditional?
Gary Karshner

St. Mary's University
San Antonio, Texas
KARSHNER@STMARYTX.EDU