Conjunctions and disjunctions

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

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

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:

$R\equiv P\wedge Q$

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:

$S\equiv P\vee Q$