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Social media provides a valuable lens for assessing public perceptions and opinions. This paper focuses on the concept of truthfulness stance, which evaluates whether a textual utterance affirms, disputes, or remains neutral or indifferent toward a factual claim. Our systematic analysis fills a gap in the existing literature by offering the first in-depth conceptual framework encompassing various definitions of stance. We introduce RATSD (Retrieval Augmented Truthfulness Stance Detection), a novel method that leverages large language models (LLMs) with retrieval-augmented generation (RAG) to enhance the contextual understanding of tweets in relation to claims. RATSD is evaluated on TSD-CT, our newly developed dataset containing 3,105 claim-tweet pairs, along with existing benchmark datasets. Our experiment results demonstrate that RATSD outperforms state-of-the-art methods, achieving a significant increase in Macro-F1 score on TSD-CT. Our contributions establish a foundation for advancing research in misinformation analysis and provide valuable tools for understanding public perceptions in digital discourse.