What is the clearest and most concrete illustration of the difference between Necessary & Sufficient Conditions found in an office setting?
Suppose someone counts as an 'manager' if s/he runs a team of +30 people. Then running a team of +30 people is a sufficient condition for counting as a manager.
Suppose also that someone without a team counts as a manager if her/ his responsibilities mean that s/he reports direct to the CEO. Here again is a sufficient condition for counting as a manager.
Suppose also - we're nearly there - that no-one counts as an executive unless they either run a team of 30+ people or, without a team, report direct to the CEO. It is then a necessary condition for being a manager that one either run a team of 30+ people or, without a team, report direct to the CEO.
A necessary condition for x is something that must happen in order for x to happen. You can think of it as, “x will never happen unless this gets done” (but even if it does, x still might not happen). Examples would include “being on time to work every day is necessary for me to get that promotion” (but you still might not get it if there is someone more qualified than you), and “avoiding Larry is necessary for me to enjoy my lunch” (but you might still have a bad lunch because your sandwich has tuna fish in it).
A sufficient condition for y is something that will definitely cause y to happen. For instance, “removing the toner cartridge will definitely prevent the photocopier from working”, or “indiscrete and illegal tax evasion will definitely lead to an unpleasant audit at some point in the future”.
It is easy to find sufficient conditions when you are looking to damage something, as in my examples, but sometimes much harder to state them positively. For example, “what is a sufficient condition to ensure the growth of the company?” In practical terms, there probably isn’t one—you might do everything right and still not make enough profit to survive. However, there are many conditions which seem necessary, such as satisfying the customer and avoiding class action lawsuits, so you might as well focus on those.
Why an "office setting?" That only adds to the confusion. Consider the following example from everyday life.
The following are equivalent statements:
- If it is raining, then it is cloudy.
- At the moment, it is not both raining and not cloudy.
- Cloudiness is a necessary condition for it raining.
- It raining is a sufficient condition for cloudiness.
Neither of the above means that raining causes cloudiness, or that cloudiness causes it to rain.
To be comfortable in an office setting, you require oxygen. But you also require the temperature to be above 60 degrees F. So oxygen is necessary, but insufficient.