Tuesday, May 16, 2017

necessary and sufficient conditions


Necessary conditions:

X is a necessary condition for Y means, 

if we don't have X, then we don't have Y, or without X, you won't have Y

To say that X is a necessary condition for Y does not mean that X guarantees Y

Having gasoline in my car (I have a gasoline engine) is a necessary condition for my car to start. Without gasoline (x) my car (y) will not start. Of course, 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.

Being 18 years of age is a necessary condition for being able to buy cigarettes legally in North Carolina. Yet, being 18 years of age does not guarantee that a person will buy cigarettes. There are many other conditions that lead to a person buying cigarettes than being 18 years of age.

Sufficient conditions:

X is a sufficient condition for Y means,

if there is X, then Y happens (X guarantees Y)

Rain pouring from the sky is a sufficient condition for the ground to be wet.
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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?