The given statement is false. Receptors that bind the neurotransmitter at the postsynaptic cell membrane are not voltage-gated.
There are two types of receptors at the postsynaptic cell membranes that can bind with neurotransmitters. The two types of receptors are ionotropic receptors and metabotropic receptors. The ionotropic receptors are ligand-gated receptors. The metabotropic receptors are G-protein coupled receptors.
Therefore, the receptors at the postsynaptic cell membrane are not voltage-gated but are the one that are ligand-gated.
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