**Instructions:** Answer all questions in the spaces provided. Show your work! Good luck! **Problem Statement:** Consider the relation \( R = \{(1,2), (2,1), (2,3), (3,4), (4,1)\} \) on the set \(\{1,2,3,4\}\). **Explanation:** This problem presents a relation \( R \) which consists of a set of ordered pairs. Analyze this relation in various contexts, such as determining properties like reflexivity, symmetry, transitivity, or exploring its representation using graphs or matrices. The image contains three mathematical problems related to set theory and relations. Here is the text transcription suitable for an educational website: 7. Find the matrix representing \( R \cup R^2 \). 8. Find the reflexive closure of \( R \). 9. Find the symmetric closure of \( R \). Each of these problems involves understanding and manipulating binary relations represented either in matrix form or through closure operations.

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