Conjunctions and disjunctions

[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:

$S \equiv P \lor Q$