q p ~ p → ~ q
Valid
Argument
type
1
(
Modus
Ponens
)
:
p
?
-
-
-
-
-
-
-
-
-
-
-
-
q
~q q ~ →
Valid
Argument
type
2
(
Modus
Tollens
)
p
?
-
-
-
-
-
-
-
-
-
Invalid Valid2 Valid1
a
?
b
a
-
-
-
-
-
-
-
-
b
Argument
Valid2 Invalid Valid1
a
?
b
b
-
-
-
-
-
-
-
-
a
Argumen
t
Valid2 Valid1 Invalid
a
?
b
~b
-
-
-
-
-
-
-
-
~a
Argumen
t
Valid2 Invalid Valid1
a
?
b
~a
-
-
-
-
-
-
-
-
~b
Argumen
t
valid2 b b c c valid invalid
All
college
students
read
books
.
(
If
you
are
a
college
student
(
c
)
then
you
read
books
(
b
)
)
.
I
am
a
college
student
.
So
,
I
read
books
.
?
_________
Valid
or
invalid
?
~ b invalid valid1 c ~ valid b c
All
college
students
read
books
.
(
If
you
are
a
college
student
(
c
)
then
you
read
books
(
b
)
)
.
I
do
not
read
books
.
So
,
I
am
not
a
college
student
.
?
____
Valid
or
invalid
?
valid s invalid valid2 h s h
If
you
are
a
student
(
s
)
then
you
do
homework
(
h
)
.
I
am
a
student
.
So
,
I
do
homework
.
?
-
-
-
-
-
-
-
-
Valid
or
invalid
?
invalid s ~ h valid1 s ~ h valid
If
you
are
a
student
(
s
)
then
you
do
homework
(
h
)
.
I
do
not
do
homework
.
So
,
I
am
not
a
student
.
?
-
-
-
-
-
-
-
-
Valid
or
invalid
?
valid2 invalid a valid s s a
All
squirrels
like
apples
.
(
If
this
creature
is
a
squirrel
(
s
)
then
she
likes
apples
(
a
)
)
.
This
creature
is
a
squirrel
.
So
,
she
likes
apples
.
?
-
-
-
-
-
-
Valid
or
invalid
?
invali i r valid1 r i valid2
If
it
is
raining
(
r
)
then
we
stay
inside
(
i
)
.
We
stay
inside
.
So
,
it
is
raining
.
?
-
-
-
-
-
-
Valid
or
invalid
?
p h ~ valid2 invali valid1 ~ h p
If
I
promise
to
help
(
p
)
then
I
will
help
(
h
)
.
I
did
not
promise
to
help
.
So
,
I
wont
help
.
?
-
-
-
-
-
-
-
Valid
or
invalid
?
h valid1 Invali valid2 ~ d d h ~
If
I
have
homework
due
tomorrow
(
d
)
then
I
do
my
homework
(
h
)
.
I
do
not
have
homework
due
tomorrow
.
So
,
I
won't
do
my
homework
.
?
-
-
-
-
-
-
Valid
or
invalid
?