A previous study on students approach to problems of Set Theory in Iran brought me somehypotheses. These encouraged me to test the hypotheses in this supplementary study. Mypurpose of this study was to consider some students' cognitive difficulties in Set Theory. Iinvestigated students’ conceptual understanding of two major concepts of Set Theory – theconcepts of inclusion and belonging. I also studied the ways students use Venn diagram tofigure out problems in Set Theory. I wanted to examine how students figure out the differentmeanings of words in the natural and formal language. To do so, I analyzed six experiments. Icompared three experiments with the experiments of my previous study in Iran. My researchquestions suggested using a qualitative research method. My theoretical framework built aroundtheories of semiotic activities, which were used in the analysis.The results indicated that students can make unfortunate use of Euler–Venn diagrams. A set ofsets was a difficult concept for students. Some words in natural language, even the word "set" inboth natural and formal language, caused confusion for students when introduced in Settheoretic contexts. Students failed sometimes to distinguish between sets and elements. Theexperiments showed that students’ cultural context had affect on students' cognition regardingmathematical objects.