The sufficient condition should be placed on the left side of the arrow and the necessary condition should be placed on the right side of the arrow.

sufficient condition → necessary condition

But how do we know when a condition is sufficient or necessary?

A sufficient condition is a condition that is enough to guarantee the conclusion, but it is not necessary in guaranteeing the solution.

example:

All cats are mammals.

Mike is a cat.

Therefore, Mike is a mammal.

sufficient condition → necessary condition

cat → mammal

Mike = cat

therefore: Mike →. mammal

In the example above we are stating that Mike being a cat is enough to guarantee(sufficient) that Mike is a mammal. Why? Because "All cats are mammals".

On the other hand, a necessary condition is required to guarantee(necessary) the conclusion, but it is not sufficient on its own to guarantee the conclusion.

example:

All cats are mammals.

Mike is not a mammal.

Therefore, Mike is not a cat.

In the example being a mammal is required to guarantee being a cat. According to the argument you cannot be a cat and not be a mammal. It's more clear if I say:

All cats are mammals.

Mike is a cat.

Mike is not a mammal.

Therefore, Mike is a cat and not a mammal.

But Mike can't both me a cat and not a mammal because the argument declares that "all cats are mammals". Is it easier to see why "mammal" is a necessary condition now?

Kumar example stumped me! I confused BEING LATE with being CITED AS LATE. It took me 20 minutes to sort out what was going on in my head. The mistake I made was assuming a sufficient condition when there was not one. The condition I assumed was "If you are caught late you will be cited" and I assumed that Kumar was caught.

Being CITED as late is a sufficient condition for being more than 5 minutes LATE.

But being LATE is NOT a sufficient condition for being CITED as late.

You can be LATE and not get CITED for it.

But you can't be CITED for being late if you were never LATE in the first place.

An example that is more clear is this:

People are cited as "speeding" only if they are going 10 mph over the speed limit.

Sam was going 25 mph over the speed limit.

Therefore, Sam will get a speeding ticket.

Going 10mph over the speed limit is a necessary condition for getting a speeding ticket.

But, it is not a sufficient condition in getting a speeding ticket. We are not given a sufficient condition in this argument that would guarantee the conclusion that "Sam will get a speeding ticket". The flaw in the argument is that its author assumed that going 10mph over the speed limit would guarantee that Sam gets a speeding ticket. However, the only thing that can guarantee Sam getting a speeding ticket, is Sam getting a speeding ticket.