Using R Shiny to Provide the Same Feedback for Different Iterations of the Same Data

Question

I run a doggy daycare and I need to keep track of which dogs are allowed to be in the same room and which dogs are not allowed in the same room. With this information, I want to create an R Shiny dashboard that others can access to check if certain groups of dogs are compatible or not. Here is my current dataset:

x <- list(Dog1 = c("Rocky", "Rocky", "Rocky", "Rocky", "Rocky"), 
 Dog2 = c("Toast", "Toast", "Pippa", "Kevin", "Walter"), 
 Dog3 = c("Pippa", "Pippa", "Kevin", "Walter", "Casper"), 
 Dog4 = c("Casper", "Walter", "Walter", "Otis", "Mila"),
 Compatible = c("YES", "YES", "NO", "NO", "YES"))

dogGroups <- as.data.frame(x)

I would like to create a dashboard in which a user is able to select four names (in any order) and get a "YES" or "NO" in return. As you can see in the data frame, Rocky, Toast, Pippa, and Casper are compatible. If someone were to select those dogs, in that order, they would see that "YES", they are compatible. However, I would also like to make it so if they chose those individuals in the order of Pippa, Toast, Casper, and Rocky, they would still get a "YES". I would like that to be the case for all rows.

Any tips on how I should go about doing this? I'm somewhat new to R and R Shiny so I may be missing things. Thanks for any help!