What logical principle is illustrated by the rule: If A = B and B = C, then A = C?

• A. Modus Ponens
• B. Law of Noncontradiction
• C. Transitivity of Equality
• D. Identity

Answer: (C)

Transitivity of equality states that if A equals B and B equals C, then A equals C. This is the substitution principle for equality: you can replace equals with equals along a chain. Since B is the same as both A and C, A and C must be the same as well. In formal terms, equality is an equivalence relation with properties including transitivity, which is precisely what this rule expresses.

The other options don’t fit because Modus Ponens handles a conditional claim and its antecedent, not chains of equality. The Law of Noncontradiction concerns a statement and its negation, not how objects relate through equality. Identity (reflexivity) says every object is equal to itself, which is a weaker property than the chaining captured by transitivity.