Conjunctions and disjunctions

Here we introduce two more formal symbols. Consider the following propositions:

$ \begin{array}{l} P : \text{Socrates ate an apple.} \ Q: \text{Socrates ate an orange.} \ R: \text{Socrates ate an apple and an orange.}\ S: \text{Socrates ate an apple or an orange, or both.}\ \end{array} $

The last two propositions are combinations of the two first.\(R\) is true if and only if both \(P\) and \(Q\) are true. We call this a conjunction, and represent it by the following:

\(R \equiv P \land Q \)

Similarly, \(S\) is true if \(P\) is true, or if \(Q\) is true, or if both are true.\(S\) will be false only if both \(P\) and \(Q\) are false. We call this a disjunction, and represent it by the following:

\(S \equiv P \lor Q\)