Final answer:
T cell-independent activation of B cells occurs when B cell receptors (BCRs) interact with T-independent antigens, providing the first signal for activation. This process does not require signals from T cells. Toll-like receptors and factors from the complement system provide the second signal in T cell-independent activation.
Step-by-step explanation:
T cell-independent activation of B cells occurs when B cell receptors (BCRs) interact with T-independent antigens, such as polysaccharide capsules or lipopolysaccharides. These antigens have repetitive epitope units that allow for cross-linkage of multiple BCRs, providing the first signal for activation. In T cell-independent activation, the second signal comes from toll-like receptors or factors from the complement system, since T cells are not involved.