MGF1106

1
MGF1106
Unit One Ex. 2.9-2.11 Objectives 39 40
2
Ex. 2.9-2.11
Objective 39
To reach a logical conclusion to make an argument
valid.
3
Valid argument forms
1. Modus Ponens p ? q
p

?
q
?
p
4
A ? B A______
If the Braves win, then they will lead the
division. The Braves win. ?
?
B
They lead the division.
If you do not attend class, then you will be
withdrawn. You do not attend class. ?
?C ? D ?C_____ ?
D
You will be withdrawn.
5
2. Modus Tollens p ? q
q
q
p
You must be outside the larger circle.
Therefore, you must be outside the smaller circle.
6
A ? B ?B____ ?
If Alice goes to the mall, then she will buy
something. She did not buy something.
?A
Alice did not go to the mall.
?A ? ?B B_______ ?
If I dont like apples, then I dont like
bananas. I like bananas.
I like apples.
A
7
3. Historical Syllogism p ? q
q ? r
p ? r
r
q
p
8
?A ? ?B ?B ? ?C ?
If we dont win, then class will not be
dismissed. If class is not dismissed, then I
cant go swimming. ?
?A ? ?C
If we dont win, then I cant go swimming.
9
4. Disjunctive Syllogism p ? q
p
p
q
?
x
x
x
You must be in one of the regions marked with x.
You are not in circle p.
Therefore, you must be in q.
10
I like to play the piano or I like to sing. I do
not like to sing. ?
A
I like to play the piano.
11
p
q
x
You must be in the region marked with x.
Therefore, you must be in p.
Therefore, you must be in q.
12
B
A
I like to cook and I like to swim. ?
I like to swim.
I like to cook.
13
Select the conclusion that will make the
following argument valid.
If I prepare dinner for the family, then they
will eat. If they eat, then they are not hungry.
Symbolize each premise
d ? e
First premise
e ? ? h
Second premise
d ? ? h
Conclusion
If I prepare dinner, then they are not hungry.
14
If all teachers are good teachers, then no
student needs tutoring. Some students need
tutoring.
p all teachers are good teachers
q no student needs tutoring
p ? q
1st premise
? q
2nd premise
? p
Conclusion
Some teachers are not good teachers.
15
I have blue eyes or I have red hair. I do not
have red hair.
p I have blue eyes.
q I have red hair.
p ? q
1st premise
? q
2nd premise
p
Conclusion
I have blue eyes.
16
Ex. 2.9-2.11
Objective 40
To determine if arguments are valid or invalid.
17
Determine if the argument is valid or invalid.
Invalid
18
Determine if the argument is valid or invalid.
Valid
19
Determine if the argument is valid or invalid.
Valid
20
Determine if the argument is valid or invalid.
Invalid