Need help translating idea in math formula

Hi all, I need some help with 2 problems that I have. I have 2 ideas, related to set theory, and I would like to translate these ideas from words to math. Could you help me with that? How to translate the following 2 definitions into math?

- Definition 1 "Relevant Result": proportion of the list that contains at least 1 item from the list of Y, out of the total number of results for the query.

- Definition 2: proportion of the list that contains all items from the list of Y, so there is a perfect match, out the total number of "Relevant Results" according to Definition 1.

Both definitions are related to each other, but are at the same time separate metrics. Thanks!