Three presynpatic neurons, X, Y and Z, synapse on a postsynaptic neuron via a chemical synapse. Draw out this situation. When presynaptic neuron X is stimulated, the postsynaptic cell membrane becomes slightly depolarized. When presynaptic neuron Y is stimulated, the postsynaptic cell membrane becomes slightly hyperpolarized. When presynaptic neuron Z is stimulated, the postsynaptic cell becomes more positive

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.