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YOU are better than YOU think. Show
yourself how:
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Read logic
chapters 1 to 5 in online volume Three
Skills for Algebra for greater skills & confidence
in work
and study.
Learn to read notes and textbooks like
a lawyer, so that no nuance, no subtlety and no clause escapes your
attention. |
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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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Shorthand or Symbols as Pronouns
Chapter 20
Previous: Chapter 19. Symbols
& Logic
1 Pronouns and Shorthand Symbols
The words it, you, I, he and she are pronouns. They can be used
to refer to objects or individuals. Further, from time to time, these pronouns
are used to refer to different objects and different people. The meaning of each
pronoun can last for just a short while, before the given meaning is forgotten
or changed. Pronouns and nicknames provide short ways for talking and writing
about objects and people. Pronouns provide a form of shorthand. Got it?
2 Pronouns and Shorthand Labels
There is only one pronoun it. For each object we meet or have met, we
could say it. But if I say it, which object do I mean? The word it
is easily overused. The single pronoun it is not enough for us. We
need more.
To overcome this difficulty of not having enough pronouns, we may invent our
own names, labels or pronouns for people and objects. Then in speaking about a
person or object, we use a name, label or individual pronoun. Here letters and
other symbols (the choice is wide) can serve as short names, labels or extra
pronouns. We can have one name or pronoun for each person or object we talk
about.
In logic, we can talk about events like (i) Aunt Jane visits, (ii) the cat
climbs a tree, or (iii) Tom plays. In speaking about one of these events we
could use the pronoun it, or we could mention the name of the event, or
we could provide a temporary (?) shorthand label. For example, we can talk about
event A, or event B. The shorthand letters here serve as names or extra
pronouns. So we can say event A, or event B, or event M. For more labels, we can
number the people or objects. This further helps to identify them. For instance,
we can refer to the first situation A, the second situation B, the third
situation C .... Doing both, that is assigning numbers and labels is acceptable,
although this introduces redundancy.
3 Shorthand Notation
One way implication rules can be written in many forms. For instance, the
four phrases in the left column of the following table all have the same
meaning. To avoid writing these phrases in their longhand form, we can use
compact, or more compact shorthand notation (symbols), etc.
| Phrase |
Shorthand Notation |
| if A then B |
A Þ B |
| A implies B |
A Þ B |
| B if A |
B Ü A |
| B is implied by A |
B Ü A |
Compact forms for the shorthand phrase A if and only if B are given by
A iff B and by AÛ B. In place
of A if and only if B, we may say situation A is equivalent to situation
B or, more briefly, A is equivalent to B. The four phrases in the left
column of the next table all have the same meaning and the same shorthand form.
| Phrase |
Shorthand Notation |
| A is equivalent to B |
A Û B |
| A if and only if B |
A Û B |
| A iff B |
A Û B |
| A when and only when B |
A Û B |
The four phrases and the shorthand notation A Û
B are interchangeable. We can use one in place of any other as we like or
just for the sake of variety while talking or writing.
Next: Chapter 21, Occurrence
Tables - a prequel to truth tables.
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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.
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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