Final answer:
The statement is false because enzymes like acetylcholinesterase degrade neurotransmitters within the synaptic gap rather than within the sub-synaptic membrane.
Step-by-step explanation:
The statement "Several mechanisms can remove the neurotransmitter, such as being inactivated by specific enzymes within the sub-synaptic membrane" is false. Although several mechanisms do indeed remove neurotransmitters from the synaptic cleft to avoid continuous stimulation of the postsynaptic neuron, which would make it less likely to fire an action potential, the specific location and process slightly differ from the statement given. The neurotransmitters are removed by three primary processes: diffusion away from the synaptic cleft, enzymatic degradation within the synaptic cleft, and reuptake also known as recycling by the presynaptic neuron. Enzymes such as acetylcholinesterase act within the synaptic gap to degrade neurotransmitters like acetylcholine and terminate the signal, rather than within the sub-synaptic membrane.