Consider the following documents: d$1$: Information retrieval literature normally speaks of terms and queries; d$2$: The Boolean retrieval model is a model for information retrieval; d$3$: Pose any query which is in the form of a Boolean expression of terms; d$4$: Our goal is to develop a system to address the ad hoc queries; and d$5$: A document is relevant if it is one that the user perceives as containing information of value.

Construct a term$-$document incidence matrix for the above documents. Normalize words by converting uppercase to lowercase and reduce word forms to their root form $($e$.$g$.,$ query and queries are reduced to query$).$ Ignore stop words $$ grammaticaConsider the document corpus of question $5.$ Construct an inverted index for the document corpus. As in question $5,$ perform text normalization. What is the length of the smallest postings list?