Final answer:
The statement is false. B cells mature in the bone marrow and T cells mature in the thymus gland, after which they travel to secondary lymphoid organs.
Step-by-step explanation:
The statement is false. All lymphocytes originate from immature cells in the red bone marrow. However, their maturation processes differ based on the type. B cells mature within the bone marrow itself, while T cells migrate to the thymus gland where they undergo a critical development process. Upon maturation, B cells remain in the bone marrow before traveling to the circulatory and lymphatic systems, and T cells move from the thymus to various secondary lymphoid organs.