While Large Language Models (LLMs) have become central tools in various fields, they often provide inaccurate or false information. This study examines user preferences regarding falsehood responses from LLMs. Specifically, we evaluate preferences for LLM responses where false statements are explicitly marked versus unmarked responses and preferences for confident falsehoods compared to LLM disclaimers acknowledging a lack of knowledge. Additionally, we investigate how requiring users to assess the truthfulness of statements influences these preferences. Surprisingly, 61\% of users prefer unmarked falsehood responses over marked ones, and 69\% prefer confident falsehoods over LLMs admitting lack of knowledge. In all our experiments, a total of 300 users participated, contributing valuable data to our analysis and conclusions. When users are required to evaluate the truthfulness of statements, preferences for unmarked and falsehood responses decrease slightly but remain high. These findings suggest that user preferences, which influence LLM training via feedback mechanisms, may inadvertently encourage the generation of falsehoods. Future research should address the ethical and practical implications of aligning LLM behavior with such preferences.