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  title: 'Conjunctions and disjunctions',
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  text: '[summary: "P and Q" is written $P \\land Q$, "P or Q" is written $P \\lor Q$.]\n\nHere we introduce two more formal symbols. Consider the following propositions:\n\n>  $ \\begin{array}{l}\nP : \\text{Socrates ate an apple.}  \\\\\nQ: \\text{Socrates ate an orange.} \\\\\nR: \\text{Socrates ate an apple and an orange.}\\\\\nS: \\text{Socrates ate an apple or an orange, or both.}\\\\\n\\end{array} $\n\nThe 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:\n\n> $R \\equiv P \\land Q $\n\nSimilarly, $S$ 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:\n\n> $S \\equiv P \\lor Q$',
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