For a given search, a document search and retrieval system searched a library of $12000$

documents, and presented the user with $3000$ documents out of which the user found only $2000$ to be

relevant. The user was told that actually there were a total of $4000$ documents relevant to that search.

Determine $($i$)$ TP$,$ TN$,$ FP$,$ FN$,$ confusion matrix $($ii$)$ Recall and Precision $($iii$)$ True positive rate and

False positive rate $($iv$)$ Sensitivity and specificity