

Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
The concepts of biconditional and exclusive or statements in logic, including their definitions and truth tables. It also provides exercises to prove the equivalence of certain logical statements. Misusing conditional statements and disjunctions are common errors in logic, and this document clarifies the differences between these logical operators.
Typology: Schemes and Mind Maps
1 / 3
This page cannot be seen from the preview
Don't miss anything!
Part 2 Module 2 Extension: The Biconditional and the Exclusive Or Two common sources of error in logic involve misusing conditional statements and misuing disjunctions. A typical misuse of conditional statements is confusing a conditional with its converse or its inverse. A typical misuse of disjunctions is failure to realize that “or” in logic is inclusive. Anothrer way of stating it is to say that a typical error in logic is confusing a conditional statement with a biconditional statement, and a second typical error is confusing a disjunction with an exclusive disjunction. Biconditional statements A biconditional statement is a statement of the form “ p, if and only if q .” This is denoted p ↔ q , and is sometimes abbreviated “ p iff q .” Definition : A biconditional statement is true, only when the two terms have the same value. Exclusive disjunctions An exclusive disjunction , more simply called an exlcusive or , is a statement of the form “ p or q (but not both) .” This is denoted p ⊕ q , and is sometimes abbreviated “ p xor q .” Definition: An exclusive or statement is true, only when exactly one of the two terms is true. This truth table illustrates the definitions of the biconditional and exclusive or propositions. p q (^) p ↔ q p ⊕ q T T T F T F F T F T F T F F T F
Exercises 1 -‐3: Use a truth table to prove each of the following:
!