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Is it possible to create a saved search for customers who have purchased x item.
And customers who have purchased y, z item but never the x item ?

Doing a search on sales order.
How it will be possible I am not exactly sure. Even with grouping and stuff.

use summary criteria and group your results by customer.
something like
`CASE WHEN {transaction.item} IN (_item_y_internalid_, _item_z_internalid_) THEN 1 END`  SUM, Formula(Numeric), greater than 0
`CASE WHEN {transaction.item} = _item_x_internalid_ THEN 1 END`  SUM, Formula(Numeric), equal to 0

:point_up: assumes a customer search, but you could do it as a transaction search instead

Transaction search will give you more flexibility, you have more options for join table option. Because transactions touches more tables than entities

Yes I did it on transaction search only. 
I never had previously used summary criteria so   was not sure how it worked.
Wanted to try saved search before moving towards suiteQL.