Final answer:
Transmitter-gated ion channels in the membrane of a post-synaptic cell alter the ion permeability of the postsynaptic membrane, which can depolarize the postsynaptic membrane.
Step-by-step explanation:
When transmitter-gated ion channels in the membrane of a post-synaptic cell open in response to neurotransmitter binding, they alter the ion permeability of the postsynaptic membrane, which in turn may depolarize the postsynaptic membrane. This depolarization is called an excitatory postsynaptic potential (EPSP) and makes the postsynaptic neuron more likely to fire an action potential. In contrast, inhibitory neurotransmitters cause inhibitory postsynaptic potentials (IPSPs), which hyperpolarize the postsynaptic membrane and make the neuron less likely to fire an action potential. Therefore, option A, alter the ion permeability of the postsynaptic membrane, which in turn may depolarize the postsynaptic membrane is the correct answer.