[summary: "P and Q" is written $~$P \land Q$~$, "P or Q" is written $~$P \lor Q$~$.]
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$~$