Assertion and Reason Analysis: Precision and Recall

This section evaluates the truthfulness of the given Assertion (A) and Reason (R) concerning metrics used in information retrieval.

Evaluating Assertion (A)

Assertion (A) states: Precision is the fraction of the documents retrieved that are relevant to the user’s information need.

• Definition of Precision: Precision measures the relevance of the search results. It is calculated as the ratio of the number of relevant documents retrieved to the total number of documents retrieved by the system.
• Truthfulness: The statement accurately defines precision. Therefore, Assertion (A) is true.

Evaluating Reason (R)

Reason (R) states: In practical situations, recall and precision are always inversely related.

• Relationship between Recall and Precision: Recall is the fraction of relevant documents that are retrieved out of all the relevant documents that exist. While there is often a trade-off between recall and precision (improving one may decrease the other), this relationship is not *always* inverse.
• Counterexample: It's possible to improve both metrics simultaneously, especially when a system is suboptimal. For instance, refining a search algorithm might retrieve more relevant documents (increasing recall) without significantly increasing irrelevant ones (maintaining or increasing precision).
• Truthfulness: The claim that they are *always* inversely related is an oversimplification and thus incorrect. Therefore, Reason (R) is false.

Conclusion

Based on the analysis:

• Assertion (A) is true.
• Reason (R) is false.

This corresponds to the option where (A) is true and (R) is false.