Finding Conflicting Combinations Using SQL
SELECT Boy_Name, Girl_Name
FROM Everyone_Loves_Relationships
GROUP BY Boy_Name, Girl_Name
HAVING COUNT(DISTINCT Relationship_Status) = 2


This query assumes that none another value (including NULL) is present in Relationship_Status field. If this is not true then replace the condition with

HAVING SUM(DISTINCT CASE WHEN Relationship_Status = 'Yes'
                         THEN 1
                         WHEN Relationship_Status = 'No'
                         THEN 2
                         ELSE 3
                         END) &lt; 3