home
***
CD-ROM
|
disk
|
FTP
|
other
***
search
/
Software of the Month Club 1995 December
/
SOFM_Dec1995.bin
/
pc
/
win
/
edu
/
easi_ps
/
qs27.sdy
< prev
next >
Wrap
Text File
|
1995-10-31
|
3KB
|
78 lines
"Sets/Logic Chpt 2 (Logic)"
"Define a proposition "
"
statements of mathematical content whose truth value
is unambiguous.
(We may not KNOW the value, but it is definitely T or F) "
"The 'logical connectives' are: "
"not ~ strongest connective
and ^ { mid-
or v strongest }
if...,then --> weakest connective
(also xor)
material equivalence <--> "
"Stuffier names for the logical connectives are: "
"
not negation
and conjunction
or disjunction
--> material implication, conditional of p & q "
"Describe 'material equivalence'"
"defined in terms of other connectives:
p <--> q means (p --> q) ^ (q --> p)
two PROPOSITIONS are material equivalent iff they have
the same TRUTH VALUE "
"Define an 'atom' "
"a propositional variable which may be T or F
also called an 'atomic proposition "
"Define a 'propositional formula' "
"the joining of propositional variables by logical connectives "
"The rules for 'propositional formulas' are: "
"1. T and F are prop formulas
2. each atom is a prop formula
3. For all atoms a and b, the following are prop-forms
~a
a v b
a ^ b
a-->b
4. if a form has n different atoms, its Ttable has 2en rows"
"Define 'logical equivalence'"
"
f1 <==> f2 iff f1 ==> f2 and f2 ==> f1
if f1 <==> f2 - THEY HAVE THE SAME Ttable [ T(f1) = T(f2) ]
As in sets for all prop-forms a, b, c
- a <==> a
- if a <==> b, then b <==> a
- if a <==> b, and b <==> c, then a <==> c "
"What is the difference between 'logical equivalence' and
'material equivalence' ? "
"
logical equiv. is a relation between prop-forms.
if f <==> g, it means f and g have the same Ttable
^^^^^^^ ^^^^^^
material equiv. is a relation between props
if f <--> g, it means they have the same Tvalue
^^^^^^ ^^^^^^"
"Define a 'tautology' "
"a prop-form that is True on every line of its Ttable
Notes: f1 ==> f2 iff (f1) --> (f2) is a tautology
f1 <=> f2 iff (f1) <-> (f2) is a tautology
some examples: T
(a v ~a)
(a v b) v ((~a) ^ (~b))
(a -> b) <-> ((~a) v b) "
"Define a 'contradiction' "
"
a prop-form that is False on every line of its Ttable.
sometimes defined as the negation of a tautology "