Employ an online or offline tutor at your own risk from
AU:
tutorfinder.com.au
CDN : findatutor.ca
CDN: .i-tutor.ca
CDN: Montreal Tutors
NZ: findatutor.co.nz
UK: tutorhunt.com
UK: tutors4me.co.uk
USA: wiziq.com
USA: ziizoo.com
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YOU are better than YOU think. Show yourself how:
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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
Do not leave here without it - Logic
mastery will develops critical thinking, improve reading and writing,
and give a firmer base for work and studies at many levels. Good luck.
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Caution: Site advice is approximately
correct, for some circumstances, not all. Site How-TOs are logically
developed, but not tried and tested. That leaves room for thought and
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After logic,
(a) continue reading Three
Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving
linear2007 Equations ; or (b) see this calculus
starter lesson and Volume 3, Why
Slopes & More Math, chapters 2 to 6;
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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Explore collaborative whiteboards from
groupboard, twiddla or
scriblink.
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Chapter 8, Part II
Previous: Chapter 8,
Part I.
Two-Way Implication Rules
In the previous chapter Implication
Rules, we met the rule
Tom goes out to play
when and only when
Aunt Jane visits his home.
This is an example of a two-way rule. Two-way rules can also be said or
presented in different ways. Again the form of a rule does not matter, provided
we recognize exactly what is meant. The above rule also can be rewritten (or
restated, again without changing its meaning) in the if-and-only-if form:
Aunt Jane visits her nephew Tom's home
if and only if
Tom goes out to play.
This form suggests we call such rules biconditional statements. The
prefix bi- here signals two ways. Whenever the condition (or situation) Aunt
Jane visits her nephew Tom's home occurs, the other condition (or situation)
Tom goes out to play must also occur, and vice-versa, if this rule is to
be never-disobeyed.
You may prefer to say if and only if instead of when and only when.
For instance, I might say or suggest to you: I will do that for you if and only
if you do this for me. Alternatively, I might say or suggest to you: I will do
that for you when and only when you do this for me. Tone provides the only
difference between the two suggestions. Both of these suggestions represent a
two-way obligation to which we might agree. Confusion or disappointment or false
expectations may happen when suggestions such as these are not explicitly
accepted or rejected.
Two-Way or Two One-Way Rules
The two-way Aunt Jane and nephew Tom rule above is rewritten (with no change
in meaning) as
Aunt Jane visits her nephew Tom's home implies Tom goes out to play,
and also that
Tom goes out to play implies Aunt Jane visits her nephew Tom's home.
In this form, the two-way rule is seen to be the same as two one-way
implication rules, each going in the opposite direction.
Chapter Subsections: [ Up ] [ More on Two-Way Implications ] [ Equivalent Situations or Conditions ]
Next: Stating and Writing 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.
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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