Talk:High School Mathematics Extensions/Logic

Those extra steps
I cannot agree with putting in those extra steps, they are omitted for a purpose. It is to force the reader to think actively about the intermediate steps, so that he/she is more involved in the learning process. This book is never meant to be a passive experience, those steps must be removed. The reader must struggle with how we arrive at a result inorder to learn. Zhuo 15:09, 24 Dec 2003 (UTC)
 * Second thought, those extra steps are not harmful.Zhuo 15:14, 24 Dec 2003 (UTC)

an error?
at 2.3.1 Simplification it is written:

\begin{matrix} (x + y)(x' + y') &=& x(x' + y') + y(x' + y')\\ &=& xx' + x'y' + yx' + yy'\\ \end{matrix} $$

but shouldn't it be



\begin{matrix} (x + y)(x' + y') &=& x(x' + y') + y(x' + y')\\ &=& xx' + xy' + yx' + yy'\\ \end{matrix} $$ (xy' instead of x'y')? --jan


 * Yes, fixing. r3m0t (cont) (talk) 20:04, 21 May 2004 (UTC)


 * but but the rest of this doesn't work anymore --jan


 * Oh... I'll rewrite it completely. Or you can. r3m0t (cont) (talk) 21:34, 21 May 2004 (UTC)

I consider this chapter to be done
I deleted some material and now i consider this chapter to be done.Xiaodai 04:29, 5 Jul 2004 (UTC)

My Kudos...
Thanks! very interesting and informative...

Reasons for Particular Interest
In "Laws of Boolean Algebra, Simplification", you mention, quote: "From those two examples we can see that complex-looking expressions can be reduced very significantly. Of particular interest are expressions of the form of a sum-of-product [...]"

I think it would be of interest (no pun intented *g*) to mention where (as in what field) SOP terms are of particular interest, e.g. to reduce the often lengthy expressions as obtained by solving Karnaugh Maps (maybe other fields do distract a beginner less, though). Probably also a few more words on the why would be of interest, e.g.: in practical calculations, each AND, OR and NOT comes at certain costs (which may differ in hardware and software design); thus the goal must me to reduce the overall cost. (This also would introduce the notion cost in a pretty elegant way, which could be elaborated some more, e.g.: circuit design with NAND logic vs. implementation cost in software requiring NOT and AND etc.)

Just a few thoughts on an overall really nice article. Gulliveig 16:13, 8 January 2007 (UTC)

mistake?
In section 2.3.1 (Laws of Boolean Algebra/Simplification), after the message saying "If the next step is unclear, try constructing truth tables [...]," the statement xy + z + x'y' is simplified to 1. I don't understand why; the statement is false if x=0, y=1, and z=0. Could someone please clarify this?

24.6.101.190 02:35, 18 November 2007 (UTC)


 * Now that you point it out, I see you are right.
 * I deleted that last erroneous line in the "proof".
 * Should we leave it like that, ending at xy + z + x'y' with no further simplification possible?
 * Or should we modify the starting point and all the intermediate statements so that it actually does reduce down to 1?
 * --DavidCary (talk) 18:48, 2 September 2008 (UTC)

AND - an Operator a function ?
I'm referring to the Table where x an y assume different states i.e - T or F. The heading is given as "AND Function". "AND" is a logical operator, it's never a function.

More introduction?
The name of this section is "logic". There was a very short intro to logic in general, then you jumped into Boolean logic. To make this page more self-contained, it seems that the basics of logic themselves should be explained at the beginning. Perhaps there is another page that you could refer the reader to? In the middle of the page, you explain "proposition". This part could be moved up to the first section. Then, you could explain "AND" and "OR". Then, your tables in Section 2 would make more sense to an uninformed reader. I'm keeping in mind that the beauty of such pages is that students who have not learned this material before can teach themselves from this.Lizmaemom (discuss • contribs) 23:49, 3 July 2011 (UTC)