We investigate the age of information (AoI) of a relay-assisted cooperative communication system, where a source node sends status update packets to the destination node as timely as possible with the aid of a relay node. For time-slotted systems without relaying, prior works have shown that the source should generate and send a new packet to the destination every time slot to minimize the average AoI, regardless of whether the destination has successfully decoded the packet in the previous slot. However, when a dedicated relay is involved, whether the relay can improve the AoI performance requires an in-depth study. In particular, the packet generation and transmission strategy of the source should be carefully designed to cooperate with the relay. Depending on whether the source and the relay are allowed to transmit simultaneously, two relay-assisted schemes are investigated: time division multiple access (TDMA) and non-orthogonal multiple access (NOMA) schemes. A key challenge in deriving their theoretical average AoI is that the destination has different probabilities of successfully receiving an update packet in different time slots. We model each scheme using a Markov chain to derive the corresponding closed-form average AoI. Interestingly, our theoretical analysis indicates that the relay-assisted schemes can only outperform the non-relay scheme in average AoI when the signal-to-noise ratio of the source-destination link is below -2dB. Furthermore, comparing the merits of relay-assisted schemes, simulation results show that the TDMA scheme has a lower energy consumption, while the NOMA counterpart typically achieves a lower average AoI.