Final answer:
In the context of mathematics for economics, a necessary condition is something that must be satisfied for an event to take place, while a sufficient condition is one that, if satisfied, guarantees an event occurs. Option B is correct: A necessary condition is always a prerequisite for an event to happen, whereas a sufficient condition alone guarantees the event's occurrence.
Step-by-step explanation:
In the context of calculus for economics, a necessary condition and a sufficient condition are concepts that define the prerequisites and guarantees for an event to occur. A necessary condition is something that must be true for an event to happen; without it, the event cannot occur. In contrast, a sufficient condition alone can ensure the event's occurrence—meaning its presence guarantees that the event will take place. Therefore, the correct answer to the question is B) A necessary condition is always a prerequisite for an event to happen, while a sufficient condition alone guarantees the event's occurrence.
For example, in economics, having demand for a product is a necessary condition for a sale to occur, as you can't typically sell a product with no demand. However, demand alone may not be a sufficient condition because even if demand exists, other factors like price and availability may prevent the sale. Conversely, a sufficient condition could be having demand coupled with the right price and availability, which together would guarantee that a sale will happen.