Or in Sufficient Condition and Necessary Condition

gemandlight

For example:
if N or M is selected, S is out.

Since or is in the sufficient condition, N and M are INDEPENDENTLY sufficient for S. So does that mean we can have just N selected, just M selected or both selected?

Also another example:
If S is out, N or M is selected.

Since or is in the necessary condition, N and M and JOINTLY necessary for S. What does that mean? Does that mean we need N and M BOTH to be selected? We can't have just N or just M selected? I'm so confused about this concept when applying to logic games... Please help, thanks!

c.janson35

N or M--> S

If N is in, S is in.
If M is in, S is also in.
If N and M are in, S is still in, because each is enough by themselves to guarantee S; having both of them is like a double whammy.

/S-->N or M

This means that if /S, then either N or M or both must be in (because or is inclusive). So, this means that if /S is true, and /N is true, then M must be in because we need one of them. This also means that if /S is true and /M is true, the N must be in because again we need one of them. What we can't have is the scenario in which /S occurs and both N and M are also out.

gemandlight

@c.janson35 Thanks for your reply! So for /S --> N or M, even though the or is jointly necessary for /S, we can have just N in or M in? What does jointly necessary refer to in this case because I interpreted it as N AND M have to be both in. Thanks again!