Statement Attempt 1:
It seemed to ignore everything and get products from anywhere regardless of country
SELECT *
FROM products
WHERE `country` = 'America' AND
product = 'Product 1' AND
product = 'Product 2' AND
completed = 'complete'
Statement Attempt 2:
The result of this was that is returned 0 results, even though the results are there hypothetically.
SELECT *
FROM products
WHERE `country` = 'America' AND
product = 'Product 1' OR
product = 'Product 2' AND
completed = 'complete'
Your first query is logically incorrect due to product = product 1 AND product = product 2
, where clause filter rows one by one, so a single row at same time cannot contain both values in product column.
OR
criteria so it ignores the country filter if there is product 2 with status completed in another country , to correct your query you need to group your OR
criteria by using parenthesis (condition 1 or condition 2) and some other condition
SELECT *
FROM products
WHERE `country` = 'America'
AND (product = 'Product 1' OR product = 'Product 2')
AND completed = 'complete'
Or you could use IN
clause to simplify your criteria
SELECT *
FROM products
WHERE `country` = 'America'
AND product IN('Product 1','Product 2')
AND completed = 'complete'