Final answer:
The Epicureans, as part of their Hellenistic philosophy, truly denied the existence of an afterlife, focusing instead on seeking pleasure and tranquility by living in the present and reducing pain and fear.
Step-by-step explanation:
The statement that the Hellenistic philosophical school of the Epicureans denied the existence of an afterlife is true. The Epicureans believed that the purpose of life was to pursue pleasure, which they understood as a state of tranquility and freedom from pain and fear, rather than indulgence in excess.
Epicurus and his followers viewed death as the end of consciousness and sensation, negating the fear of an afterlife. Their focus was on living a fulfilling life in the present, rather than concerning oneself with the events after death. Epicurean philosophy advocated for living a life free from the distractions of politics and unnecessary desires.