Understanding the ∣{d∈D:t∈d}∣ Expression in IDF

In the expression ∣{d∈D:t∈d}∣

• {}: denotes a set.
• d∈D: means "document d is in the set D" (i.e., d is one of the documents in the corpus D).
• t∈d means "term t is in document d" (i.e., the term t appears in the document d).
• : can be read as "such that".

So, {d∈D:t∈d} describes the set of all documents d in the corpus D such that the term t appears in d.

In plain English, it represents the set of all documents where the term t appears. The outer ∣∣ then calculates the size of this set, which means it counts the number of documents that contain the term t.