Final answer:
Translating natural language sentences into predicate formulas involves using universal quantifiers, treating equations as meaningful sentences, identifying knowns and unknowns, solving equations, and verifying the reasonableness of the answer.
Step-by-step explanation:
Translating sentences in natural language into predicate formulas is a fundamental process in mathematical logic, used to express precise concepts. When you encounter phrases like "for all, for every, for any, for each," it's important to use a universal quantifier. Equations should be viewed as sentences that convey significant ideas, not just as tools for computation. The process involves identifying what is given or can be inferred (the knowns) and then solving for the quantity that needs to be determined (the unknowns). Moreover, a universal statement inherently carries with it logical relations such as necessity and sufficiency and can be disproven with a single counterexample.
When solving problems, it's also helpful to think in terms of a translational analog to understand motion equations better. Once you have the known values, they can be substituted into the appropriate equation to find a numerical solution, which should include appropriate units, ensuring validity. Lastly, simplify the algebra by eliminating terms and verify that the final answer is reasonable and makes sense within the context of the problem.