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The significant objective of this research is to recognize how to calculate the classification process using rough set theory (RST) for the Human immunodeficiency virus infection and acquired immune deficiency syndrome (HIV & AIDS) symptoms dataset. RST has a multi-dimensional concept with multiple approaches. In this paper, our main objective is to find the symptoms of (HIV & AIDS) using basic RST and Homotopy Analysis Method (HAM) to validate our claim using statistical techniques. We prefer RST & HAM over other soft computing techniques and Mathematical Modelling as both RST and Homotopy Analysis (HAM) because RST can handle vague and imprecise data efficiently, and HAM is a suitable technique for finding analytical solutions. We have used the chi-squared test to validate our claim.