Class notes
Inclusive Disjunction in Propositional Logic
- Course
- Institution
This lecture notes discusses the topic "inclusive disjunction", a compound statement or proposition that is connected by the words “Either…or” or just “or.”
[Show more]
Seller
Follow
jeffocs
Reviews received
Content preview
Inclusive Disjunction in Propositional LogicA disjunction or disjunctive statement is a compound statement or proposition that is
connected by the words “Either…or” or just “or.”
And the component statements in a disjunction are called “disjuncts.” There are two
types of disjunctive statements used in symbolic logic, namely: inclusive and exclusive
disjunction. In this post, I will only focus on inclusive disjunction.
As I discussed in my other notes titled “Propositions and Symbols Used in Propositional
or Symbolic Logic (see http://philonotes.com/index.php/2018/02/02/symbolic-logic/),
the symbol for the connective “Either…or” is v (wedge).
Inclusive disjunction uses the connective “Either…or, perhaps both.” Consider the
example below.
Either Jake is sleeping or Robert is studying, perhaps both. (J, R)
If we let J stand for “Jake is sleeping” and R for “Robert is studying,” then the statement
“Either Jake is sleeping or Robert is studying, perhaps both”is symbolized as follows:
JvR
Please note that the constants J and R do not just represent Jake and Robert
respectively; rather, they represent the entire statement. Thus, J represents “Jake is
sleeping,” while R represents “Robert is studying.”
It must also be noted that in most cases, the phrase “perhaps both” in an inclusive
disjunction is not written in the statement. Thus, in determining whether the statement
is an inclusive or an exclusive disjunction, we just need to analyze the statement per se.
Let us consider this example:
Either Jake is sleeping or Robert is studying.
As we notice, the statement does not contain the phrase “perhaps both.” But if we
analyze the statement, it is clear that it is an inclusive disjunction because it is possible
for the two component statements, namely, “Jake is sleeping” and “Robert is studying,”
to occur at the same time. (Please note that I will discuss the nature and characteristics
of an exclusive disjunction in my next post.)
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller jeffocs. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $3.49. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
48072 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 15 years now