kdb/q Count column-pair instances within a table and return all with particular condition

I have a sales records table that looks like this:

Name	Item	Action	Price
Ann	Apple	Buy	5.00
Ann	Apple	Sell	6.00
Ann	Bread	Sell	9.00
Bob	Apple	Buy	5.00
Bob	Salt	Buy	1.00
Bob	Salt	Buy	1.00
Bob	Salt	Sell	2.00

sample_data: ([] Name: `Ann`Ann`Ann`Bob`Bob`Bob`Bob; Item: `Apple`Apple`Bread`Apple`Salt`Salt`Salt; Action: `Buy`Sell`Sell`Buy`Buy`Buy`Sell; Price: 5.00 6.00 9.00 5.00 1.00 1.00 2.00)

My end result is to get the combination of Names and Items that have been both bought and sold at least once.

My thought process is to create a table like the one below, which collects the number of buys and sells for each Name-Item pair:

Name	Item	Buys	Sells
Ann	Apple	1	1
Ann	Bread	0	1
Bob	Apple	1	0
Bob	Salt	2	1

Then, extract only those Name-Item pairs that have >=1 Buys and Sells:

Name	Item
Ann	Apple
Bob	Salt

Solution

An fby might be the simplest way:

q)select distinct Name,Item from sample_data where({all`Buy`Sell in x};Action)fby([]Name;Item)
Name Item
----------
Ann  Apple
Bob  Salt