Sum and product of 2 partitions of a set

Question

There was this question in my Discrete Maths exam:

Let S={1,2,3,4,5,6}. 2 partitions P1 and P2 are given as:

P1={(1,2,3),(4,6),(5)}

P2={(1,2),(3,4,5),(6)}

Define and find the sum and product of these 2 partitions P1 and P2.

I simply thought it was just the unions and intersections of these 2 sets. But after going through many books and online resources, I cannot find anything to validate my method. Please tell how are these 2 operations defined on partitions of sets.

EDIT: Please don't just randomly downvote the question if you dont know the answer. It increases the probability that someone who might be knowing the answer may end up ignoring it.

Answer 1

I've found a definition of the product here.

The product of two set partitions B and C is defined as the set partition whose parts are the nonempty intersections between each part of B and each part of C. This product is also the infimum of B and C in the classical set partition lattice (that is, the coarsest set partition which is finer than each of B and C). Consequently, inf acts as an alias for this method.

Look at that page for an example. Presumably, the sum is the dual of the product, namely the finest partition coarser than both.

I know these operations by the names "meet" and "join". If you have difficulty figuring out what's going on, look up lattice orders. I think you'll be able to figure things out from the link I posted, but feel free to ping me if you have questions.