Rule Diagramming Confusion.

[lizk89]

Bear with me with this question.

On page 186, the text teaches us about multiple sufficient and necessary conditions. In the case that they appear, we are told to draw a conditional statement and use terms such as "and" or "or". The contrapositive is the opposite term we used initially. That much I understand.

However, when it came down to diagram the actual games toward the end of the section, the explanations seemed to use a different mode of diagramming.
For example, on page 223, one of the game rules states; "If both G and S are reduced, W is also reduced." The rule is then simply diagrammed as "GS W." Why is it stated this way?
Take another example, the next rule states, "If N is reduced, neither R nor S is reduced." Instead of a conditional statement with two necessary conditions connected by the word "and" the rule is diagrammed "N R" and "N S." How come?

Another example, page, 235, rule states: "Neither Ty nor Raimundo appears in any photograph that Wendy appears in." Instead of a conditional statement with Ty and Raimundo as two necessary conditions attached by the word "and", the rule is diagrammed as W T and W R.

And lastly, page 245, "Any language learned by the linguist or palaeontologist is not learned by the geologist." These rules are diagrammed as an LG not block and a PG not block. Why is not diagrammed as a conditional statement with two sufficient conditions L and P.

Clearly, I'm a little slow. Some help would really help.

[lizk89]

Page 249, "If Jays, Martins or both are in the forest, then so are harriers." is another example. The explanations diagram the rule as J H and M H. Why not in a conditional statement with two sufficient conditions of "Jays and Martins" H.

Is this all just an easier way of diagramming the conditional statement?

THANKS!

[Steve Stein]

Thanks for your question--that's an interesting one. There are often several ways to relay a concept, all equally valid. For example, saying that "I am always present in class" is the same as saying that "I am never absent from class."

Similarly, when it comes to conditional reasoning, the same concept can be legitimately relayed in different ways, as you correctly pointed out.

So, if I say that, if either Bobby or Cindy is at the party, Dave will not be at the party, I can diagram that as one rule (with an "or), or as two separate rules. Both characterizations are legitimate, so I would recommend using the one that you feel makes the most sense to you intuitively.

On a related note, if Ed and Frank don't get along, we could diagram that as one simple rule showing that the two don't get along (Ed Frank), or, equally legitimately, as the two sides of a standard conditional:

Ed NO Frank, and
Frank NO Ed.

Let me know whether that help helps

Thanks!

~Steve

[lizk89]

Steve,

Your help has helped! Much appreciated!

[buyer3700]

But then it changes the contrapositive.

If both G and S W the contrapositive would be NOT W NOT G or S

But in this new way

If GS W the contrapositvie would look like NOT W NOT GS you lose the "or". By leaving them grouped together doesn't that keep it as an "and"?

[Josh DeBottis]

It is still correct. You have to think through what "Not GS" means - it means not having both G and S, which means that you are missing either G or S. Hence, "Not GS" = "Not G or Not S".

As was pointed out above, there are many different ways to draw these statements, and the key is just to figure out what works best for you. If you are comfortable with the complex logic, then stick with that.

One note of caution: when negating the "and" make sure to carry over each not. What I mean is more clearly illustrated below.

"If both G and S W, then the contrapositive would be NOT W NOT G or S"

The "NOT G or S" could easily be read the same as "NOT G and NOT S/Not G nor S". To avoid this problem, you are better off illustrating the contrapositive as "Not G or not S"