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We are given a set of 24 textbooks and their coverage of three topics:

- P = 8 (Books covering Compilers)
- Q = 13 (Books covering Data Structures)
- R = 13 (Books covering Operating Systems)
- n(P ∩ Q) = 3 (Books covering both Compilers and Data Structures)
- n(P ∩ R) = 3 (Books covering both Compilers and Operating Systems)
- n(Q ∩ R) = 6 (Books covering both Data Structures and Operating Systems)
- n(P ∩ Q ∩ R) = 2 (Books covering all three topics)
- Total books = 24


We need to determine how many books have no material on Compilers (i.e., books that belong to Q, R, or neither, but not P).

Step 1: Apply Inclusion-Exclusion Formula
The total number of books covering at least one topic is given by:

n(P ∪ Q ∪ R) = n(P) + n(Q) + n(R) - n(P ∩ Q) - n(P ∩ R) - n(Q ∩ R) + n(P ∩ Q ∩ R)

Substituting the values:

n(P ∪ Q ∪ R) = 8 + 13 + 13 - 3 - 3 - 6 + 2 = 24

Thus, all 24 books cover at least one topic, meaning there are no books that do not cover any of the three topics.

Step 2: Find Books That Do Not Cover Compilers
We need to count the books that do not belong to P (Compilers). This means we are looking for books in Q ∪ R:

n(Q ∪ R) = n(Q) + n(R) - n(Q ∩ R)

n(Q ∪ R) = 13 + 13 - 6 = 20

So, the number of books that do not cover Compilers (P) is 20.

Step 3: Final Answer
Thus, the number of textbooks that do not cover Compilers is:

20

If the question intends to ask how many books only cover Q or R (excluding P), we need to further subtract books covering P ∩ Q and P ∩ R:

n(Q ∪ R) - (n(P ∩ Q) + n(P ∩ R) - n(P ∩ Q ∩ R))

= 20 - (3 + 3 - 2) = 20 - 4 = 16

Thus, the correct answer among the options given is 16.