PHIL110 Critical Thinking – SPS CUNY
Unit 10 Discussion Assignment
Take a Break!
This assignment first asks you to "Take a Break with Elmo and Big Bird." If you're not familiar
with these Sesame Street characters, watch this video.
Now that we’ve established our context, let’s have some fun with Elmo, Big Bird and sentential
logic (SL), also known as propositional logic. Let’s remind ourselves of several features of SL:
• SL is a truth-functional logic, in the sense that every statement has only one truth value --
it must be either true or false.
• An atomic sentence is a sentence that contains no sentential connectives.
• A compound sentence is a sentence that contains one or more sentential connectives.
• The truth value of a compound sentence is a function of the sentential connectives it
contains.
• Each sentential connective has a co
esponding truth table which makes explicit the
circumstances under which it is considered true (or false)
Conjunction (frequently rendered as "and") &
Disjunction (frequently rendered as "or") ∨
Negation (frequently rendered as "not") ~
Conditional (frequently rendered as "if ... then") ⊃
Biconditional (frequently rendered as "if and only if") ≡
Let’s now consider the following set of propositions:
• Elmo is red.
• Big Bird is green.
• Either Elmo is red or Big Bird is green.
• Big Bird is green and Elmo is red.
• It is not the case that Big Bird is green
Once we know the truth-value of the first two sentences (whether they are true or false), we can
establish the truth-values of the others by applying the rules for their respective connectives.
For this assignment, complete the worksheet below and add it to the Discussion Forum. Then
ead and comment on at least two students’ posts by reviewing the accuracy of their truth tables.
Worksheet
(Complete, then copy and paste the entire worksheet or the truth tables into the Discussion
Forum as your post)
Step 1. Represent these statements with variables and symbols. (For example, E could stand for
“Elmo is red,” and B for “Big Bird is green,” but feel free to change these variables per your own
preference). Complete this table below:
Here are the sentential connectives of SL and their co
esponding symbols:
https:
youtu.be/PzFXfvZuLK0
PHIL110 Critical Thinking – SPS CUNY
Given Sentence Your Formal Representation
Elmo is red. E
Big Bird is green. B
Either Elmo is red or Big Bird is green.
Big Bird is green and Elmo is red.
It is not the case that Big Bird is green
Step 2. Complete the following simple table with four combinations of T and F, where T stands
for "true" and F stands for "false." Use the standard a
ay as explained in our text.
E B
Step 3. Now complete the truth table for the rest of the sentences (again, T stands for "true,"
and F stands for "false"). The color-coding will help you determine where some of the same
information can be transfe
ed over from the previous tables.
Elmo is
ed
Big Bird is
green.
Either Elmo is red or
Big Bird is green.
Big Bird is green
and Elmo is red.
It is not the case that
Big Bird is green
E B
PHIL110 Critical Thinking – SPS CUNY
Step 4.
Interpret what this truth table tells you. What’s your claim regarding Elmo and Big Bird’s
colors using the truth table you constructed? Does the information (T and F) from your truth
table align with reality? How is the process of constructing a truth table useful?
End of the Worksheet
Recommendations for Success and Grading Criteria:
• Respond to the assignment with clear and detailed answers.
• Follow all assignment prompts and answer all prompt questions.
• Incorporate relevant examples and evidence to support your claims.
• Compose your response in clear and grammatically co
ect English and post it on time.
• Respond to other students with substantive comments and follow-up
questions.
• Acknowledge all students who commented on your post.
Editable Worksheet
Complete, then copy and paste the entire worksheet or the truth tables into the Discussion Forum as your post
Step 1. Represent these statements with variables and symbols. (For example E could stand for “Elmo is red,” and B for “Big Bird is green,” but feel free to change these variables per your own preference). Complete this table below:
Given Sentence
Your Formal Representation
Elmo is red.
E
Big Bird is green.
B
Either Elmo is red or Big Bird is green.
Big Bird is green and Elmo is red.
It is not the case that Big Bird is green
Step 2. Complete the following simple table with four combinations of T and F, when T (stands for true) and F (for false):
E
B
Step 3. Now complete the Truth Table for the rest of the sentences (T stands for true, and F stands for false). The color-coding will help you determine where some of the same information can be transfe
ed over from the previous tables.
Elmo is red
Big Bird is green.
Either Elmo is red or Big Bird is green.
Big Bird is green and Elmo is red.
It is not the case that Big Bird is green
E
B
Step 4.
Interpret what this Truth table tells you. What’s your claim regarding Elmo and Big Bird’s colors using the truth table you constructed? Does the information (T and F) from your Truth Table align with reality? How is this process and constructing a Truth Table useful?