The synapse between neuron X and the postsynaptic neuron is most likely a cholinergic synapse. Neurotransmitters from neuron X bind to the postsynaptic membrane receptors that are connected to sodium channels. Positive sodium ions(Na+)enter the cell but are not enough to make the membrane potential reach the threshold. This is an excitatory synapse.
The synapse between neuron Y and the postsynaptic neuron is an inhibitory synapse. The most common inhibitory neurotransmitter is GABA(Gamma amino butryric acid). When GABA binds to the postsynaptic receptor, chlorine channels are open. Chlorine(Cl-) is an anion that is negatively charged. When chlorine enters the cell it makes the potential go below the resting membrane potential.
The synapse between neuron Z and the postsynaptic neuron has pretty much the same mechanism as the synapse between neuron X and the postsynaptic neuron but more sodium ions enter the cell so an action potential can be generated.