In this paper, we investigate a cooperative communication system comprised of a source, a destination, and multiple decode-and-forward (DF) relays in the presence of a potential malicious eavesdropper is within or without the coverage area of the source. Based on the more general Nakagami-m fading channels, we analyze the security performance of the single-relay selection and multi-relay selection schemes for protecting the source against eavesdropping. In the single-relay selection scheme, only the best relay is chosen to assist in the source transmission. Differing from the single-relay selection, multi-relay selection scheme allows multiple relays to forward the source to the destination. We also consider the classic direct transmission as a benchmark scheme to compare with the two relay selection schemes. We derive the exact closed-form expressions of outage probability (OP) and intercept probability (IP) for the direct transmission, the single-relay selection as well as the multi-relay selection scheme over Nakagami-m fading channel when the eavesdropper is within and without the coverage area of the source. Moreover, the security-reliability tradeoff (SRT) of these three schemes are also analyzed. It is verified that the SRT of the multi-relay selection consistently outperforms the single-relay selection, which of both the single-relay and multi-relay selection schemes outperform the direct transmission when the number of relays is large, no matter the eavesdropper is within or without the coverage of the source. In addition, as the number of DF relays increases, the SRT of relay selection schemes improve notably. However, the SRT of both two relay selection approaches become worse when the eavesdropper is within the coverage area of the source.