Final answer:
The BCM theory by Bienenstock, Cooper, and Munro suggested that LTD occurs at synapses that are active when the postsynaptic neuron is weakly depolarized, and that changes in synaptic strength are specific to the active synapses during neurotransmission.
Step-by-step explanation:
The BCM theory proposed by Bienenstock, Cooper, and Munro provided insights into the bidirectional nature of synaptic plasticity, specifically in regard to long-term potentiation (LTP) and long-term depression (LTD). According to the theory, synapses that are active when the postsynaptic cell is only weakly depolarized by other inputs undergo LTD instead of LTP. This implies that synaptic efficacy can decrease (LTD) under certain conditions of synaptic activity and postsynaptic cell depolarization. Instead, a strong postsynaptic depolarization, with synaptic stimulation, leads to the strengthening of synapses (LTP).
In the context of the BCM theory and the information provided, the correct answer to the student's question is the third option: LTD occurs when synapses that are active when the postsynaptic cell is only weakly depolarized by other inputs undergo LTD instead of LTP. Additionally, the theory acknowledges the importance of input specificity, which is the idea that changes in synaptic strength in response to activity are specific to the particular synapses that are active during that time.