Exam 1 Review sheet:
An argument is factually correct if and only if all the premises are true.
An argument is valid if and only if it is impossible for all the premises to be true, but the
conclusion false.
An argument is sound if and only if it is factually correct and valid.
A classical syllogism has two premises and a conclusion. Its logical terms are ‘all’,
‘some’, ‘only’, ‘none’ and ‘are’. Its descriptive terms are names of classes (e.g. dogs,
blue things).
E.g. All dogs are cats
All cats are feet
/ All dogs are feet
This is NOT factually correct since both its premises are false (it would not be factually
true even if only one of its premises were false).
This is valid since if the premises are all true, then it is impossible for the conclusion to
be false.
This is NOT sound since it is not factually correct (it must both be valid and factually
correct to be sound).
Sentential Logic:
v (disjunction, ‘or’)
~ (negation, ‘not)
(conditional, means ‘if…,then…)
The biconditional is written like the conditional but with an arrow at
the beginning as well I don’t know how to do this on the computer!! It means, “if and
only if”.
Descriptive terms are upper case letters that abbreviate statements.
An upper case letter without any connectives is called a simple formula e.g. A
When connectives are involved, you have a complex formula e.g. ~A; A v B
The truth value of complex formulas depends on the truth value of the simple formula(s)
that make it up, together with the meaning of the connectives involved.
To see the relation between the truth value of the complex formula and its constituent
simple formula(s) we use truth tables:
E.g. (A
The truth value of this complex formula will depend on the truth value assigned to A, B,
and on the way the connectives involved (the conditional and conjunction) relate A, B.
Drawing a truth table enables us to see the relationship between the truth value of the
simple formulas and the complex formula itself.
To create the truth table first we create a table with a separate column for each letter and
connective. The number of rows is determined by how many possible combinations of
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View Full Documenttruth values there are. When there are two letters, as here, one needs four rows because
there are four possible allocation of truth values to A, B.
When writing out the truth table make sure that you are consistent in your assignment of
truth values to each letter. E.g. in the table below A appears twice: be sure that you assign
the same truth value to A in each row.
(A
B)
A
T
T
T
T
F
T
F
T
F
F
F
F
Next, one fills in the blanks, dealing with the connective at the deepest level first (the
more parentheses around a connective, the deeper it is). Here the deepest connective is
the conditional, so we do this first. To fill this in you need to know the rule for when a
conditional is true of false on the basis of the truth value of the formulas it connects. The
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 Spring '08
 Morgan
 Logic, Logical connective, Truth value, Sentential Logic

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