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YOU are better than YOU think. Show yourself how:
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-/[]\- Logic chapters 1 to 5 re- appear not in sequence, as is or longer, in Volume 1A, Pattern Based Reason, Bon Appetite. Logic
Mastery Logic mastery makes the hard, easier. Logic mastery leads to better, stronger and richer comprehension. Logic mastery improves reading and writing. Logic mastery ease learning difficulties. Logic mastery gives a headstart. In sum, logic mastery will develops critical thinking, improve reading and writing, and give a firmer base for work and studies at many levels. Good luck. After logic, (a) continue reading Three Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving liinear Equations ; or (b) see this calculus starter lesson and Volume 3, Why Slopes & More Math, chapters 2 to 6;
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-/[]\- What may be learnt and when depends on how skills and concepts are developed. Making the hard easier and clearer will allow earlier & richer development of skills and concepts. Try the Twiddla
Whiteboard. In principle, it allows
to people to draw and chat together online on a copy of this webpage or a clean
sheet. The chat may be via text or audio. Visit www.twiddla.com
to set up whiteboards to work with the webpage of your choice. |
Putting Several Rules TogetherWe can chain or link not only two but also several implication rules together. This sometimes yields useful, new information. As an exercise, we ask the question: What happens whenever Fred the dog visits the one-tree park? Several answers are possible. Some have more details than others. All are correct. To answer the question, assume or pretend the next five implication rules are never disobeyed. Further, assume that Suzy the cat lives in the one-tree park.
All the information has been stated. We start our reasoning process. That is, we will answer the question: What happens whenever Fred the dog visits the one-tree park? To answer the question, suppose or assume Fred the dog visits the park. Then from the implication rule (2), we see that Suzy the cat climbs a tree. Next, from the implication rule (1) we see that Suzy the cat gets stuck and from the implication (4) we see that birds fly around the park. Finally from the implication (5), we note sensible worms go underground. We could list all that occurs when Fred the dog visits the park. Or, we could state only those results of Fred's visit to the park which are of most interest to us. The choice is ours. For instance, one of our possible conclusions follows:
This conclusion is not of interest unless you are a fisherman (or woman) looking for worms, sensible or not, for use as bait. The conclusion selected and stated here hides the reasoning process. That is, it hides the chain of implications leading to it. Our last conclusion does not mention the intermediate events where a cat climbs a tree and birds fly around the park. The long path by which we get conclusions shows that implication or rule-based thinking can lead to surprising results. These surprising results are true if the initial implications are also true. In the long path by which we got the conclusions, the information in the third implication (3) about Charles the human is not used. The conclusion we reached is independent of implication (3). In fact, without further information, I see no way of linking the rule about Charles with the other rules. The third rule is extra information. It can be ignored. In answering questions, we often have extra information. Indeed, you can imagine the five rules given above are stated in random positions among a list of twenty, or hundred and twenty rules. An answer to the question What happens when Fred the dog visits the one-tree park? now depends on finding the rules in the list which can be used. This is a game of hide and seek. So we have to be selective, observant or fussy in deciding or seeing what information leads to our conclusions. The scenery or route by which a conclusion is reached may contain as much useful information as the conclusion itself. A conclusion may contain a fraction of the information we could have stated or written. Being aware of the route or proof by which a conclusion is attained will sometimes suggest how more conclusions can be reached. This awareness is often more important that any conclusion we state because it allows us to state more conclusions, as needed.
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