Final answer:
Satisfiability of a well-formed formula in mathematical logic is the concept of determining whether there's a set of truth values that make the formula hold true. The importance lies in understanding the principles, aiding in deriving truths from well-formed statements, akin to knowing the composition of compounds in chemistry for determining empirical or molecular formulas.
Step-by-step explanation:
The satisfiability of a well-formed formula refers to whether there is some assignment of truth values to the variables in the formula that makes the formula true. A well-formed formula is a precise statement in mathematical logic that is constructed according to the rules of the logical language and can be evaluated in terms of truth or falsehood under a given interpretation. The process of evaluating satisfiability is central to various areas of mathematics and computer science, including the study of Boolean algebra and the theory of computation.
In other words, satisfiability is about finding a solution to the equation or formula that remains consistent with the established rules or conditions. Similar to how an equation in mathematics captures a concept and can be understood more deeply once the fundamental principles are mastered, satisfiability takes this principle into the realm of formal logic. It emphasizes the importance of understanding over memorization, as knowing the underlying principles enables one to derive or validate the truth of formulae from a place of comprehension.
When considering the importance and application of satisfiability, it's integral to remember that an equation or hypothesis is tested against empirical results and expectations to determine its validity. Recognizing the composition of compounds in chemistry, for example, aids in determining the correct empirical or molecular formulas, which are important for scientific analysis and predictions.