Set Theory and Venn Diagram Applications in Census Data Analysis for Cross River State

This study demonstrates the application of set theory and Venn diagrams as analytical tools for organising and interpreting census data relating to linguistic, ethnic, and religious demography in Cross River State, South South Nigeria, a state notable for its exceptional cultural and linguistic diversity. Cross River State is home to an estimated 60 distinct language communities, making it one of the most linguistically heterogeneous administrative units in Africa, and the systematic categorisation of overlapping demographic characteristics presents a natural application domain for set-theoretic reasoning. The study uses data from the 2006 national census, supplemented by the 2021 Nigeria Living Standards Survey and church and mosque membership records, to construct set-theoretic representations of demographic intersections across twelve randomly selected local government areas. Venn diagrams are used to visualise multi-way demographic intersections, including households that are simultaneously classified under multiple linguistic groups, religious communities, and occupational categories. The logical and computational properties of set operations including union, intersection, complement, and Cartesian product are illustrated through concrete demographic examples. The study also evaluates the potential and limitations of set-theoretic methods relative to standard statistical cross-tabulation approaches for handling complex categorical demographic data. Results suggest that Venn diagram representations enhance interpretability for non-specialist audiences including local government planners and community development officers. Keywords: set theory, Venn diagrams, census data, demography, Cross River State