Class notes
Tautologies and Contradictions
- Course
- Institution
This lecture notes discuses very briefly tautologies and contradictions in propositional or symbolic logic.
[Show more]
Seller
Follow
jeffocs
Reviews received
Content preview
Tautologies and ContradictionsIn these notes, I will briefly discuss tautologies and contradictions in propositional or
symbolic logic. But please note that this is just an introductory discussion on tautologies
and contradictions as my main intention here is just to make students in logic become
familiar with the topic under investigation.
On the one hand, a tautology is defined as a propositional formula that is true under
any circumstance. In other words, a propositional expression is a tautology if and only
if for all possible assignments of truth values to its variables its truth value is always
true.
Thus, a tautology is a proposition that is always true. Consider the following example:
Either the accused is guilty or the accused is not guilty. (p)
Obviously, the proposition is a disjunction; yet both disjuncts can be represented by the
variable p. Hence, the proposition is symbolized as follows:
p v ~p
Now, in what sense that this proposition is always true? The truth table below will prove
this point.
As we can see in the truth table above, if p is true, then ~p is false; and if p is false, then
~p is true. And if we apply the rules in both inclusive and exclusive disjunction, the
result of p v ~p is always true. If we recall our discussion on inclusive and exclusive
disjunction, we learned that an inclusive disjunction is true if at least one of the
disjuncts is true; and an exclusive disjunction is true if one disjunct is true and the other
is false, or one disjunct is false and the other is true.
Hence, there is no way that p v ~p will become false. Indeed, the propositional form p v
~p is always true.
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)
79271 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now