False positives are possible but rare due to hash collisions
When there is a collision you check to see if the object living there is the one you're trying to store. If it's not then you assume negative. If it is the object you're checking then it's positive but it's a correct positive.
If it's not the object you're checking then you evict the object living there and put in the one you're checking, thus allowing the one you evicted to cause a false negative again.
The whole system works BECAUSE of intentional collisions. If there were no collisions it would just be a hashmap and you'd have unbounded data structure size.
When there is a collision you check to see if the object living there is the one you're trying to store. If it's not then you assume negative. If it is the object you're checking then it's positive but it's a correct positive.
If it's not the object you're checking then you evict the object living there and put in the one you're checking, thus allowing the one you evicted to cause a false negative again.
The whole system works BECAUSE of intentional collisions. If there were no collisions it would just be a hashmap and you'd have unbounded data structure size.