Complete the Logical Connectives and Truth Tables Worksheet. .
logical_connectives_and_truth_tables_worksheet.pdf
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Logical Connectives and Truth Tables Worksheet
Put things in your own words unless the question asks for a direct quote.
For 1-4, translate the sentences into symbolic form. This and the next section draw mostly from
the Logical Connectives lesson, but also includes the conditional operation introduced in the
Truth Tables lesson. Use the variables provided. For example, if you see “red pandas are very
cute,” use the variable C from my list. (5 points each)
P: Red pandas make good pets.
E: Red pandas are an endangered species.
C: Red pandas are very cute.
L: Less than 100 red pandas live in the wild.
Example: Red pandas are very cute, but it is false that they make good pets.
Answer for Example: C ⋅ ~P
1. Red pandas are either very cute or make good pets.
2. If red pandas do not make good pets, then they are an endangered species.
3. If red pandas are an endangered species and less than 100 live in the wild, then they do
not make good pets.
4. Red pandas are very cute and make good pets, yet they are an endangered species.
– Worksheet continues below on the next page –
For 5-8, translate the statements into English sentences. Think of your favorite animal and use
statements about it for the variables. Have each variable represent an un-negated atomic
statement. The answers you give do not have to be true—they just have to fit the pattern of
symbols given. (5 points each)
Example: G ⊃ ~H
Answer for Example: If lions live in Africa, then they do not live in Europe.
G: Lions live in Africa
H: Lions live in Europe.
5. M ⋅ N
6. ~S
7. (A ⋅ B) ⊃ C
8. ~J ⋅ (K v L)
For 9, answer based on the course text and lesson materials.
9. What pattern of T’s and F’s in a truth table shows that an argument is invalid? (This is
what I call the “toxic pattern” in my video.) Why is it impossible for a deductive
argument to have this pattern and still be valid? (10 points)
For 10 and 11, complete the following three steps: (a) translate the argument into symbolic
form, (b) create a complete truth table for the argument, and (c) state whether the argument is
valid or invalid. (25 points each)
10. [See argument sent by email]
11. [See argument sent by email]
The arguments for 10 and 11 will be sent by Canvas message on Monday, October 28. If you
want to start sooner or lose the email, let me know and I can send them to you. I am sending
these by email since different students will have different arguments to use for these problems.
The following page has an example of how to complete a problem like 10 or 11 to show you
what kind of work is expected.
Example: If Todd has a good job, then he is able to afford a new car. Either Todd does not
have a good job or he is not able to afford a new car. So, he cannot afford a new car.
Answer for Example, part (a):
J: Todd has a good job
C: Todd is able to afford a new car
J⊃C
~J v ~C
∴ ~C
Answer for Example, part (b):
J
T
T
F
F
C
T
F
T
F
J⊃C
T T T
T F F
F T T
F T F
Answer for Example, part (c): Invalid argument
~J v ~C
~C
FTFFT
FTTTF
TFTFT
TFTTF
FT
TF
FT
TF
…
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