A family of Microsoft relational database management systems designed for ease of use.
Access is not "Excel on Steroids". It's quite different in its storage and logic! Applying Excel techniques (as in this case) will be an exercise in frustration!
That said, Access does AND and OR logic, actually IMO better than Excel does: try this query (copy and paste it into the SQL window of a new Query):
SELECT * FROM yourtable WHERE [Product Code] <> 111 AND [Product Category] IN ("Hat", "Cap")
The real solution, though, is to correctly normalize your tables, If the [Product Category] value depends on the [Product Code] you really should have a ProductCodes table with the Product Code as the Primary Key, and just store the Product Code without the Category in your SKU table; use a Query to link to the ProductCodes table to look up what a 111 should be. You're using a relational database, not a spreadsheet; life will be much easier if you use it as such!