What is a necessary condition

What does necessary and sufficient mean?

A non-math example

Under what conditions are you allowed to drive a car? Sure, you can only do that when you are at least 17. So is be at least 17 a condition for Allowed to drive. You can't do without being 17, so it's one necessary condition. But is it enough to be 17? - No, because you also have to have a driver's license and someone has to accompany you or you have to be 18 already. Let's formulate a condition that has everything it needs in terms of requirements: You must be at least 17 and have a driver's license and have a companion. Such a condition that is sufficient (old German: that is sufficient) to meet all requirements is called sufficient condition. There are also conditions that are both necessary and sufficient: For the validity of the Pythagorean theorem it is e.g. B. necessary and sufficient that the triangle is right-angled: Without the right-angledness the proposition does not apply, so it is a necessary condition. On the other hand, there are no other conditions that have to be met, so the right angles are sufficient on their own. Conditions can also be neither necessary nor sufficient: Be 18 is z. B. Neither necessary for driving a car (you may under certain conditions even at 17) nor sufficient (you still need a driver's license).

Task 1

Forabsent from schoolis the condition have fever ... (multiple selection or nothing at all is possible)

exercise 2

I saw a classified ad for a used car (cash only). The condition to have enough money is to buy the car ...

Task 3

The condition that a piece of furniture has four legs and is made of wood, is ... that it is a table.