👉 Mathematics is governed by a set of fundamental rules and principles that ensure logical consistency and clarity in problem-solving. These include the commutative, associative, and distributive properties of operations like addition and multiplication, which allow for flexible rearrangement of terms. The rules of equality, such as addition, subtraction, multiplication, and division, dictate how we can manipulate equations to maintain balance. For inequalities, similar rules apply but with the added constraint of preserving the direction of the inequality when multiplying or dividing by a negative number. Additionally, mathematical operations follow specific rules for exponents and logarithms, ensuring that powers and roots are handled correctly. The rules of set theory underpin many mathematical structures, including numbers and functions, while logical operations like conjunction (AND), disjunction (OR), and negation (NOT) form the basis of algebra. These rules collectively provide a framework for rigorous reasoning and problem-solving across various mathematical disciplines.
