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This letter considers amplify-and-forward (AF) cognitive relay networks with interference power constraint and transmit power constraint in a spectrum-sharing context. In particular, we impose the interference power constraint on secondary source node, and impose the interference power constraint and the transmit power constraint on secondary relay node. We derive the exact outage probability and the lower bound on symbol error rate (SER) of cognitive transmission over Rayleigh fading channels. Our results show that the outage probability and SER saturation phenomenons occur when the interference power constraint or the transmit power constraint reaches a specified value. Monte Carlo simulations are shown to validate the accuracy of the analytical results.