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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
Amazing, Amusing, Amorous, Delicious, Delightful, Edifying,
Strengthening Elixir.
It eases work & learning difficulties Makes the hard easier. Opens eyes.
Leads to greater precision.
in reading and
writing
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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Caution: Site advice is approximately
correct, for some circumstances, not all. That leaves room for thought |
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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.
For online automated help in senior high school maths & calculus,
visit quickmath.com For Automatic
Calculus and Algebra Help with derivatives, integrals, graphs, linear equations,
matrix algebra, visit calc101.com
With overlap, each site quickmath
& calc101offers a different range of
services, some free, some not, all based on webmathematica. Good luck.
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Occurrence Table for Material Implication, Chapter 21, Part
II
Previous: Chapter 21, Part I, Special
Use of Three Words
2 One-Way Implications
Any rule which can be stated in the form if a first situation A occurs,
then a second situation B occurs, in brief, if A then B or A
implies B, is called a one-way implication.
A one-way implication which is never disobeyed is said to hold and to be
(always) true. For a one-way implication rule if A then B, we recall the
following:
- The rule is obeyed when both situations occur.
- The rule is not disobeyed when the first situation A does not occur but
the second B occurs.
- The rule is not disobeyed when the first situation A does not occur and
also the second situation B does not occur.
- The rule is disobeyed if the first situation A occurs but the second
situation B does not.
The last two items 3 and 4 can be summarized by saying that disobeying a one-way
implication rule is impossible when the first situation A does not occur. When
not disobeyed, the rule is said to be obeyed by default. The following
table, an occurrence table for the one-way implication rule if A then B, summarizes
what has been said.
| row |
situation A |
situation B |
if A then B |
| 1 |
occurs |
occurs |
obeyed |
| 2 |
occurs |
occurs not |
disobeyed |
| 3 |
occurs not |
occurs |
not
disobeyed |
| 4 |
occurs not |
occurs not |
not
disobeyed |
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 if-then rule is obeyed,
disobeyed, or not disobeyed.
Row 2 represents the situation in which A occurs but B does not.
Observe that in this situation, the rule is disobeyed. In the situations
represented by the other three rows, the rule is not disobeyed. A one-way
implication rule if A then B is said
-
to be always true,
-
to always hold
when it is never disobeyed. The one-way implication if A then
B is always true when the situation described in row 2 in the above table
never occurs.
Remark. If situation A never occurs, the
implication rule if A then B is never disobeyed amd it is said to be
vacuously true.
Links to Chapter Sections: [Special
Use of Three Words] [ 21. Material Implication Occurrence Table ] [ Occurence Table for IFF ] [ 21. Converses for 1-Way Implications ]
Next: Chapter 21, Part III, Occurrence Table
for Two Way Implications.
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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.
Vol 1A Postscripts
- online only
+Proof by
Absurdity alias proof by contradiction
+How the demand
for consistency supports the law of the excluded middle
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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