In this paper, we consider a cognitive cooperative relay network (CCRN) that utilizes a decode-and-forward relay in the presence of multiple primary users. Given this system setting, we study the effect of multiple primary transmitters (PU-Txs) and multiple primary user receivers (PU-Rxs) on the outage probability of the considered CCRN. Specifically, power allocation policies for the secondary user transmitter (SU-Tx) and the secondary relay (SR) are formulated, subject to the outage constraint which is imposed by the PU-Rxs as well as the peak transmit power limits given at the SU-Tx and SR. On the basis of these power allocation policies for the SU-Tx and SR, an expression for the outage probability of the CCRN is derived. Numerical examples are presented to show the effect of different system parameters on the outage probability of the CCRN.