Finding mutually exclusive data to fulfill multiple criteria - algorithm

Question

I am trying to figure out an algorithm which would allow me to programmatically resolve the following problem.
There is a book club that has a set of rules for permission to join. You must have read 3 separate books which each conform to at least one of the following rules. All 3 rule criteria must be fulfilled by a separate book. Those rules are as follows:
Rules:
id
field
comparator
value
1
Author
IN
["John Steinbeck", "J.D. Salinger"]
2
Rating
>=
4.0
3
Number of Pages
>
300
The following is the list of books a user has read thus far:
Books:
id
title
author
rating
pages
1
Of Mice and Men
John Steinbeck
3.88
107
2
To Kill a Mockingbird
Harper Lee
4.28
281
3
Animal Farm
George Orwell
3.96
112
4
The Grapes of Wrath
John Steinbeck
3.98
464
5
1984
George Orwell
4.19
328
6
The Catcher in the Rye
J.D. Salinger
3.81
277
I've written a function which can allow me to check one specific rule with one specific book to return a boolean response indicating whether that book satisfies a given rule. The function is has the following signature
function is_valid(rule, book)
However, by running each book against each list of rules, I come up with the following list of books which match each rule:
rule_id
book_id
1
1
1
4
1
6
2
2
2
5
3
4
3
5
3
6
Now by manually looking through the resulting list of matching rules & books, I can tell that one of the combinations that would work is:
rule_id
book_id
1
1
2
2
3
4
Therefore the user who had read these 6 books would qualify to join the book club because they had read 3 separate books to satisfy each of the 3 rules.
What I'm hoping to find here is someone with expertise in data analysis that can help point me in the direction of an algorithm which can help me solve this problem programatically and allow me to scale this problem with many more rules and books that number in the tens of thousands potentially.
Any guidance would be greatly appreciated.