Propositional logic · Definition
Disjunction
Before you start you need to know
Disjunction joins two propositions with the inclusive "or"; its truth value depends on the truth values of both.
Definition
Given propositions \(P\) and \(Q\), their inclusive disjunction is the proposition \(P\lor Q\).
Disjunction, also called "logical or", joins two propositions with the idea of "or". It is true when at least one of them is true; it is also true when both are.
The word inclusive is important: here we are not required to choose exactly one alternative. The possibility that both are true is part of the operation.
The truth table of disjunction lets us distinguish it from other everyday uses of "or", which sometimes have an exclusive sense.
Think about it
Why can \(P\lor Q\) be true even if \(P\) and \(Q\) are both true?
Because the disjunction used here is inclusive: it requires at least one truth, not exactly one.
Exercises 10
- P ∨ Q is true when...
- If P and Q are false, P ∨ Q is...
- Which symbol represents disjunction?
- In inclusive disjunction, if P and Q are true, the result is...
- P ∨ ¬P is an example of...
- P∨Q is false only when...
- Inclusive disjunction allows...
- P∨P is equivalent to...
- Which assignment makes \(P\lor Q\) false?
- By De Morgan, ¬(P∨Q) is equivalent to...
References
- Frederic P. Schuller, Lectures on the Geometrical Anatomy of Theoretical Physics · Lecture 1, Introduction / Logic of Propositions and Predicates, YouTube, 2015.