Math 114
Logic Unit
Test Review
1) Fill in the blank
|
Connector |
Symbol |
|
Or |
|
|
And |
|
|
If-then |
|
|
Negation |
~ |
Negation each statement
2) All cats are friendly
Answer: Some cats are not friendly
3) John likes ice cream.
Answer: John does not like ice cream
Using the symbolic representations
p: The cat is friendly
q: The cat is playful
Express the following compound statements in symbolic form.
a) The cat is friendly and the cat is playful
b) Either the cat is playful or the cat isn’t friendly
c) If the cat is playful, then the cat is friendly.
Complete the each true table.
4) 
|
P |
Q |
|
|
T |
T |
T |
|
T |
F |
T |
|
F |
T |
T |
|
F |
F |
F |
5)
|
P |
Q |
|
|
T |
T |
T |
|
T |
F |
F |
|
F |
T |
F |
|
F |
F |
F |
6) 
|
p |
Q |
|
|
T |
T |
T |
|
T |
F |
F |
|
F |
T |
T |
|
F |
F |
T |
Complete each truth table
7) 
|
p |
q |
|
~p |
|
|
T |
T |
T |
F |
F |
|
T |
F |
T |
F |
F |
|
F |
T |
T |
T |
T |
|
F |
F |
F |
T |
T |
8) 
|
p |
q |
|
|
|
T |
T |
T |
T |
|
T |
F |
F |
T |
|
F |
T |
F |
T |
|
F |
F |
F |
T |
Validity
1) Write the argument in symbolic form, then determine if the argument is valid
p: you exercise regularly
q: you are healthy
If you are healthy, you exercise regularly.
You don’t exercise regularly
Therefore, you are not healthy.
If you are healthy, you exercise
regularly.
You don’t exercise regularly 
Therefore, you are not healthy. 
: hypothesis
: conclusion
|
p |
q |
|
|
|
|
|
|
T |
T |
T |
F |
F |
F |
T |
|
T |
F |
T |
F |
F |
T |
T |
|
F |
T |
F |
T |
F |
F |
T |
|
F |
F |
T |
T |
T |
T |
T |
The argument is valid
Determine if the argument uses inductive reasoning or deductive reasoning
1) Math 114 is a math course
Math courses
are fun
Math 114 is fun
Deductive reasoning
2) John had a chemistry quiz on Monday.
John had a
chemistry quiz on Wednesday
Therefore, John will have a quiz on Friday
Inductive reasoning
Solutions
to the Test 1 Review
Test 1 Review (Math
114)
Solutions
I)
Reasoning
and statements
1)
Do the
following arguments use deductive reasoning or inductive reasoning
a) Stan noticed that a plane flew over his house at 5:00 PM Monday
Stan noticed that a plane flew over his house at 5:00 PM Tuesday
Stan noticed that a plane flew
over his house at 5:00 PM Wednesday
Therefore, Stan concludes that a plane will fly over his house everyday at 5:00 PM
(Inductive reasoning)
b) All mountain ranges are scenic.
The
Therefore, the
(Deductive reasoning)
2) Negate the following statements.
a) All trees have green leaves
Negation: Some trees do not have green
leaves
b) Some food at Greasy Nicks taste good.
Negation: All
food at Greasy Nicks does not taste good.
c) John loves to play football
Negation: John does not love to play football
II)
Complete a
truth table for each statement
3) 
Solution:
|
p |
q |
~q |
|
|
T |
T |
F |
T |
|
T |
F |
T |
T |
|
F |
T |
F |
F |
|
F |
F |
T |
T |
4) 
Solution:
|
p |
q |
~p |
|
|
|
T |
T |
F |
T |
F |
|
T |
F |
F |
F |
F |
|
F |
T |
T |
T |
T |
|
F |
F |
T |
T |
T |
5) 
Solution:
|
p |
q |
~q |
|
|
|
T |
T |
F |
T |
T |
|
T |
F |
T |
T |
F |
|
F |
T |
F |
F |
F |
|
F |
F |
T |
T |
F |
III)
Use De
Morgan’s Law to negate each statement
6)
Negation: 
7) 
Negation: 
IV) Determine if the argument is valid or invalid.
8) If
John studies for his math test, he will pass the math test.
John did not pass his math test 
Therefore, john did not study for
his math test 
Argument: 
|
p |
q |
~p |
~q |
|
|
|
|
T |
T |
F |
F |
T |
F |
T |
|
T |
F |
F |
T |
F |
F |
T |
|
F |
T |
T |
F |
T |
F |
T |
|
F |
F |
T |
T |
T |
T |
T |
Invalid argument
8) If
you work hard, then you will go far in life
You work hard 
Therefore, you will go far in
life. 
Argument: 
|
p |
q |
|
|
|
|
T |
T |
T |
T |
T |
|
T |
F |
F |
F |
T |
|
F |
T |
T |
F |
T |
|
F |
F |
T |
F |
T |
This argument is a tautology, so the argument
is valid