Which statement represents a true axiom regarding equality?

The statement that represents a true axiom regarding equality is that when A equals C and B equals C, then A must equal B. This is a fundamental property of equality known as the transitive property. It indicates that if two quantities are each equal to a third quantity, they are equal to each other.

This property is a cornerstone in mathematics, ensuring consistency in relationships among quantities. For instance, if you know that two people have the same amount of money, and a third person also has the same amount as either of the first two, then it logically follows that all three individuals have the same amount of money. Such logical deductions are essential in proofs and solving equations.

The other statements do not accurately reflect established axioms regarding equality or do not hold true universally in mathematical contexts, leading to misunderstandings about the nature of equal quantities.