lecture notes9

Ifaisaknavethenbmustnotbeaknightsinceknavesalwayslieso

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Unformatted text preview: ive
ways
“p
if
and
only
if
q”
is
expressed
 in
English:
   

p
is
necessary
and
sufficient
for
q
   

if
p
then
q
,
and
conversely
   

p
iff
q
 Truth
Tables
For
Compound
 Proposi1ons
   Construction
of
a
truth
table:
   Rows
   
Need
a
row
for
every
possible
combination
of
values

 for
the

atomic
propositions.
   Columns
   Need
a
column
for
the
compound
proposition
(usually
 at
far
right)
   Need
a
column
for
the
truth
value
of
each
expression
 that
occurs
in
the
compound
proposition
as
it
is
built
 up.
   This
includes
the
atomic
propositions

 Example
Truth
Table
   Construct
a
truth
table
for


 p
 q
 r
 ¬r
 p
∨ q
 p
∨ q → ¬r
 T
 T
 T
 F
 T
 F
 T
 T
 F
 T
 T
 T
 T

 F
 T
 F
 T
 F
 T
 F
 F
 T
 T
 T
 F
 T
 T
 F...
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This document was uploaded on 03/06/2014 for the course MATH 320 at CSU Northridge.

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