Final answer:
The statement is false because B cells mature in the red bone marrow, while T cells mature in the thymus after migrating there from the bone marrow.
Step-by-step explanation:
The statement that B lymphocytes and T lymphocytes both arise in the bone marrow and remain there to undergo their maturation before migrating to organized secondary lymphoid tissues is false. While it is true that both B cells and T cells arise in the bone marrow, their maturation sites are different. B cells mature in the red bone marrow, which is reflected in the 'B' of B cells for 'bone.' On the other hand, T cells migrate from the bone marrow to the thymus, where they undergo maturation. This is why they are called T cells, with the 'T' representing 'thymus.'
After their maturation, both B cells and T cells travel through the circulatory system to secondary lymphoid organs, such as the spleen and lymph nodes, where they perform their immune functions, seeking out and responding to pathogens.