This paper introduces the concept of logical consistency in students' thinking in mathematical contexts. We present the Logical in-Consistency (LinC) instrument as a valuable assessment tool designed to examine the prevalence and types of logical inconsistencies among undergraduate students' evaluation of mathematical statements and accompanying arguments. Beyond its utility as an assessment tool, this paper also underscores the potential of the LinC instrument as an instructional aid, effective for identifying students who may inadvertently overlook logical contradictions within their mathematical assertions. Furthermore, this paper outlines a practical classroom activity based on the LinC instrument format. This activity is tailored to enhance students' capacity for reasoning with logical consistency, specifically in proof-oriented mathematics courses. We hope this activity helps instructors address and mitigate logical inconsistencies in students' thinking throughout their classroom activities.