Wednesday, August 30, 2023

Necessary and sufficient conditions


Necessary conditions:

X is a necessary condition for Y

if X is not present, Y doesn't happen.

(yet, to say that X is a necessary condition for Y does not mean that X guarantees Y)

Having gasoline in my car (gasoline engine cars) is a necessary condition for my car to start. Yet,  having gasoline in the car does not guarantee that my car will start. There are many other conditions needed for my car to start.

Having oxygen in the earth's atmosphere is a necessary condition for human life. However, having oxygen will not guarantee human life. There are many other conditions needed for human life other than oxygen in the atmosphere.


Sufficient conditions:

X is a sufficient condition for Y,

if X is present, Y happens (X guarantees Y)

Rain pouring from the sky is a sufficient condition for the ground to be wet (not necessary, since the ground could be wet for other reasons).
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Test yourself: 

*Is sunlight a necessary or sufficient condition for the flowers to bloom?

*Is earning a final grade of C a necessary or sufficient condition for passing the course?

*Is being a male a necessary or sufficient condition for being a father?

*Is having AIDS a necessary or sufficient condition for having the HIV virus?

*Is studying for a test a necessary or sufficient condition for passing a test?

*Is completing all the requirements of your degree program a necessary or sufficient condition for earning your degree?