Final answer:
Hyperpolarization would definitely not occur if many excitatory postsynaptic potentials (EPSPs) arrived at the same neuron at the same time. This is because EPSPs are depolarizing events, moving the neuron closer to the threshold, whereas hyperpolarization moves it further away.
Step-by-step explanation:
If many excitatory postsynaptic potentials (EPSPs) arrived at the same neuron at the same time, what would definitely NOT happen is B) Hyperpolarization. EPSPs are depolarizing events, meaning they make the neuron's membrane potential more positive, moving it closer to the threshold for firing an action potential. Hyperpolarization, on the other hand, is the process where the membrane potential becomes more negative, moving the neuron further from the threshold. Therefore, hyperpolarization would not occur as a result of EPSPs arriving simultaneously. When multiple EPSPs occur at the same location and close in time, it's known as temporal summation. If EPSPs are generated at multiple locations across the neuron's membrane but at the same time, this is referred to as spatial summation. Both temporal and spatial summation can lead to the neuron reaching its threshold for firing an action potential if the summed EPSPs are of sufficient strength.