Spreading truths and blocking rumors are two typical strategies for inhibiting rumors. In practice, a tradeoff between the two strategies, which is known as the TSRB strategy, may achieve a better cost-effectiveness. This paper is devoted to assessing the effectiveness of the TSRB strategy. For that purpose, an individual-level spreading model (the generic URQT model) capturing the interaction between a rumor and the truth is established. Under the model, a set of criteria for the dying out of a rumor is presented. These criteria capture the combined influence of the basic parameters and the network structures on the effectiveness of the TSRB strategy. Experimental results show that, when the rumor dies out, the dynamics of a simplified URQT model (the linear URQT model) fits well with the actual rumor-truth interacting process. Therefore, the generic URQT model and sometimes the linear URQT model provide a proper basis for assessing the effectiveness of the TSRB strategy.