How does the logical connective “or” affect the truth of a compound proposition?

In formal logic, the connective "or" is known as disjunction and functions as a truth-function, meaning the truth-value of a compound proposition depends on the truth-values of its component parts.12

There are two primary types of disjunction to consider:

• Inclusive Disjunction ($x\vee y$): This is the standard interpretation in logic. A compound proposition is true if at least one of its components is true, or if both are true. It is only false if both component propositions are false.12
• Exclusive Disjunction ($x\dot{\vee }y$): This asserts that one or the other component is true, but not both.1

The truth-value of these propositions can be determined using a truth table, which maps all possible combinations of truth and falsity for the components. For example, in an inclusive disjunction, if component $p$ is true and component $q$ is false, the resulting compound proposition $p\vee q$ is true. When evaluating arguments, disjunctions are often used to create branches in semantic tableaux, where the original disjunction is considered true if either branch is satisfied.23