lecture notes9

Solution converseifidonotgototownthenitisraining

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Unformatted text preview: 
is
 the
meaning
of
Exclusive
Or
(Xor).
In
p ⊕ q , one
of
p
and
q
must
be
true, but not both. The truth table for ⊕ is:
 p
 q
 p ⊕q
 T
 T
 F
 T
 F
 T
 F
 T
 T
 F
 F
 F
 
Implica1on
   If
p

and
q

are
propositions,
then
p →q
is
a
conditional
statement
or
 implication

which
is
read
as
“if
p,
then
q
”
and
has
this
truth
table:
 p

 q
 p →q
 T
 T
 T
 T
 F
 F
 F
 T
 T
 F
 F
 T
   Example:
If
p

denotes
“I
am
at
home.”
and
q

denotes
“It
is
 raining.”
then


p →q

denotes
“If
I
am
at
home
then
it
is
 raining.”

   In
p →q
,
p

is
the
hypothesis
(antecedent
or
premise)
and
q

is
 the
conclusion
(or
consequence).

 
Understanding
Implica1on
   In
p →q there
does
not
need
to
be
any
connection
 between
the
antecedent
or
the
consequent. The “meaning” of p →q depends
only
on
the
truth
values
 of
p
and
q.

   These
implications
are
perfectly
fine,
bu...
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