5
Logic (cont.)
5.1
Negation
•
verbally: not
p
sometimes a little messier in English: it is not the case that
p
symbolically:
∼
p
(alternatives:
¬
p
,
p
)
•
definition using a truth table
•
examples — based on flipping a coin five times
state negations of:
five heads appeared
at least one head appeared
both heads and tails appeared
5.2
Combining operations
•
precedence rules
∼
before
∧
,
∨
(latter two have equal precedence)
•
can use parentheses to alter order of evaluation
•
examples — develop truth tables for expressions like
∼
p
∧
q
p
∨
(
∼
q
∨
r
)
5.3
Creating expressions for given truth tables
•
using
∧
to write an expression with one T entry in truth table
e.g.
FFTF (
∼
p
∧
q
)
•
using
∨
to write an expression with one F value in truth table
e.g.
TFTT (
∼
p
∨
q
)
•
disjunctions of conjunctions to produce truth tables with two T entries
perhaps mention DNF
5.4
Conditional statements
•
verbally: if
p
then
q
symbolically:
p
→
q
•
terminolgy
p
is the
antecedant
,
premise
, or
hypothesis
q
is the
conclusion
or
consequence
•
develop definition with an example:
p
: you work hard
q
: you will pass this course
under what conditions would we consider the statement
p
→
q
to be
false
?
i.e.
under what circunstances could you consider me a liar if I said this?
use this to build a truth table for
p
→
q
p
q
p
→
q
T
T
T
T
F
F
F
T
T
F
F
T
try to convince them that it is reasonable
11
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•
verbal forms for
p
→
q
use an example
p
: I live in Toronto,
q
: I live in Canada
to persuade them that following forms are all equivalent
if
p
then
q
q
if
p
p
is sufficient for
q
q
follows from
p
p
only if
q
??? — be careful here
q
is necessary for
p
(follows from above)
•
precedence: lower than
∨
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 Fall '06
 Carter
 Logic

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