Final answer:
An 'undertaking' can indeed be synonymous with a 'promise,' as both terms refer to a commitment or an agreement to do something. Through historical and textual references, 'undertaking' implies a serious intention akin to a promise, further supporting the truth of the statement.
Step-by-step explanation:
True/: An "undertaking" can be synonymous with a "promise." To determine the truth of this statement, we can look at the context in which 'undertaking' is used. The word 'undertaking' often denotes a kind of agreement or a commitment to do something, which aligns closely with the definition of 'promise.' For instance, the line from "The Status of Non-Muslims Under Muslim Rule" implies a strong commitment or guarantee, implying that the undertakings are similar to promises made with serious intentions. Similarly, the statement from Cassius Dio suggests that people might make promises or undertakings, sometimes, without the intention to follow through, which suggests that undertakings can be akin to promises.
Furthermore, the phrase "With firm reliance on the protection of divine Providence, we mutually pledge to each other our Lives, our Fortunes, and our sacred Honor" reflects a solemn and serious pledge, which could also be regarded as an undertaking or a promise of significant magnitude. Hence, in various contexts, an 'undertaking' can indeed carry the meaning of a 'promise' with a sense of being bound to one's word or action.