After recognising explicit and implicit quantifiers, we now apply them to programming statements. Arrays and loops naturally create finite universes of discourse, such as index sets $\{1,2,\ldots,20\}$. A universal quantifier describes a property of every array entry, while an existential quantifier describes at least one entry with a property. In this lesson, quantifiers in programming statements will translate array properties into precise logical form.

A \textbf{quantified programming statement} is a logical statement involving arrays, loops, or indexed data that can be written using quantifiers. A universal quantifier is used when a property holds for all entries. An existential quantifier is used when a property holds for at least one entry.