https://maximummathematics.com/books/foundational-mathematics/set-theory/the-laws-of-set-theory/index.htmlUnderstanding the laws of set theory is essential because they solve the problem of determining when two or more sets are equal, through fundamental equations including associativity, commutativity, and distribution. These laws provide a structured framework for defining and manipulating sets, ensuring consistency and precision in operations such as subset, difference, and symmetric difference. In other words, by developing laws of set theory, we can essentially manipulate equations involving sets as if they were algebraic equations. In addition, the laws of set theory will allow us to convert complicated expressions involving sets into simpler ones, much like how we took complicated logical expressions and simplified them into smaller, logically equivalent expressions.Hugoen-US