6/26/23
Mation
programs
correct
-understand formal
systems
-prove
-
What
want
->
-proving
can't
correct
chips
be
proved/computed
output
or
hardware
meaningful
errors
(Intel
correct
FDIU
Bug)
Proposition
-
a
statement of fact
T
P "Toronto
is
Negation (7)
"not
p"
is
F
or
=
the
-
the
thats
Canada"
of
capital
=
7
reverses
the truth value
of
proposition
one
negation
P
of
Conjunction (n)-(p1g),"and" Iisi f
p
Note:
"but" is
expresses
logically
surprise
and
equivalent
is
to
"and,"
but
Disjunction
(v)
-
(prg)"or"(specifically
T
"inclusive or")
if
is
por g (or both)
are
either
True
none
Or))-P,*9birtefact
Tin
East
Note:informally," or" is
usually
meanta n
conditional," logical
Conditional()-(p-g)"
read
Operation
Truth
4
Table
IPI
T
-
T
f
F
I
-isi
I
proposition
of
implication,
6)
"implies", "p onlyifa
Note:Logical implication is "opposite" to
100% certain
E
door
was
opens,
button
pressed
causal
implication
Ju
press
button,
door
opens
Why
ex.
Let
consider
thus
Why
2X.
(7-T)=T?
does
p=F,
(p
-
(1
-
r
q)1(p
n(+
T)
-
T
T
1
-
f
=
+
?
()
is
g
T,
=
r)
=
p
F)
=
F
F
=
-
(qur)
(T nf)
f
=T
T
f)
-
T?
=
pistiveinline, are
Let
Let
for
for
m,
m,
psg:T,
up
p
falls,
is
-
p
contrapositive
my
is
T- T T
=
=
"
sunny
to
also false
49 -up
of
Converse
Contrapositive
Inverse
of
of
p
>
q
q p
->
is
q
T
I
T
T
7
F
F
T
I
F
T
ex
rain
clouds
-
f
Note:words
-
-
is
peg
Biconditional-(p <5g)" it
D
is
pig
is
are
and
p Lequivalent
on
"necessary"
and
"sufficient"
"sufficient" to conclude clouds (rech"suff"
"necessary"for
rain
(c*r)"nec"
Operator
Precedence (highestto lowest)
7
negation
M
conjunction
V
->
-I
disjunction
implication
bicondition
*
exclusive
or
Knights
Puzzle:
Logic
island, knights always tell
Knaves lie
scare
Ipp1,
A- "B
B-
"We
is
a
are
A
and
knight"
B
opposites"
truth,
Knaves
and
Let
p
Ais
B
=
g
lap
2)
-p
-
a)
knight
=
knight
is
(b)
q
-
52q2b)2q
P
-
-p