Final answer:
Antibodies produced by B cells function extracellularly to target and neutralize pathogens, while the elimination of intracellular pathogens is conducted by T cells; hence, antibodies do not act both intracellularly and extracellularly.
Step-by-step explanation:
The statement Antibodies can act both intracellularly and extracellularly is False. Antibodies, which are large Y-shaped proteins produced by B cells in the humoral immune response, function primarily in extracellular spaces to bind to antigens found on the outside of pathogens like bacteria and viruses. Once bound, these antigens signal for phagocytes to destroy the pathogens. B cells and antibodies cannot directly address intracellular pathogens; this function is carried out by T cells through the cell-mediated immune response. T cells target and eliminate pathogens that have managed to enter and reside inside a host’s cells.