As it is mentioned in the F1 score Wikipedia, 'F1 score reaches its best value at 1 (perfect precision and recall) and worst at 0'.
What is the worst condition that was mentioned?
Even if we consider the case of: either precision or recall is 0. The whole F1-score value becomes undefined. Because when either precision or recall is to be 0, true postives should be 0. When the true positives value becomes 0, both the precision and recall become 0.