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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. |
Chapter 21
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| row | A | NOT (A) |
| 1 | occurs | occurs not |
| 2 | occurs not | occurs |
The following table
| row | A | NOT A | NOT (NOT A) |
| 1 | occurs | occurs not | occurs |
| 2 | occurs not | occurs | occurs not |
| row | situation A | situation B | A and B |
| 1 | occurs | occurs | occurs |
| 2 | occurs | occurs not | occurs not |
| 3 | occurs not | occurs | occurs not |
| 4 | occurs not | occurs not | occurs not |
The situation A and B occurs provided
rows 2, 3 and 4 in the above never occur.
In each row, a possible combination of the occurrence or nonoccurrence of the situations A and B is shown in the middle two columns. In the last column, we put a note to say whether or not, the situation A and B occurs or occurs not.
* Language Note. The phrase A and B is also labelled (called) the conjunction of the situations A and B. The situation A and B is said to be true when and only when both the situations A and B occur (= are true).
In everyday speech when you use the word or in a phrase like John or Andrew will go to the store, the usual expectation is that only one will go, not both. But there is another use of the word or favored in logic. The word or is employed in the at least one sense (as is done in logic and mathematics). With this sense or usage, the previous phrase is understood in the inclusive sense: John or Andrew, or both, will go to the store. We now proceed and we will use the word or in the at least one sense.
The situation (A or B ) is said to occur if at least one of the two situations A and B occurs. Otherwise, it is said not to occur. This is summarized in the following table.
| row | situation A | situation B | A or B |
| 1 | occurs | occurs | occurs |
| 2 | occurs | occurs not | occurs |
| 3 | occurs not | occurs | occurs |
| 4 | occurs not | occurs not | occurs not |
The situation A or B can be said to occur
provided the situation in row 4 does not occur.
We have to be careful with the word or. Its meaning depends on the speaker and possibly the listener. That is, confusion and ambiguity results when two people in question use the same words but give them different meanings. To eliminate this ambiguity in everyday speech, write and say one of the following:
Links to Chapter Sections: [Special Use of Three Words]
Next: Occurrence Tables for Material Implications IF A THEN B
www.whyslopes.com
Volume 1A, Pattern Based Reason
Chapters 1 to 24
FOREWORD
Three Remarks
1 Introduction
2 Communication
3. Elements of Reason
4 Implication Rules
5. Deception
6 Chains of Reason
7 Longer Chains
For & From Consistency
8. Language Change
9 Next Chapters
10 Responsibility
11 Accidental Patterns
12 Knowledge Islands
13 Euclidean Logic 14 Deductive & Empirical Views of Mathematics
15 Objectivity
16 Origin of Rules
and Patterns
17 Objective Ways
18. Waking up
19. Symbols & Logic
20. Pronouns or Symbols
21. Truth Tables I.
22. Truth Tables II
22. Biconditional
22. Contrapositive
23. IF-THEN table
24. Indirect Reason Again To reason often means to persuade someone of the need for an idea or action. That someone could be yourself. So be careful.
1A Logic Postscripts
- online only+Proof by Absurdity alias proof by contradiction
+How the demand for consistency supports the law of the excluded middle
+Reality versus or with the aid of Imagination
+Links for reason, logic and crtical thinking
+Three Remarks
+History Lost or Missing
There is a difference between
knowing how to spend money,
and having money to spend.There is likewise a difference
between mastering a skill
and having meeting a situation in which it applies.
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