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Necessary and Sufficient Conditions

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Sweater Sweater Polo Heart Polo Heart Heart Polo Heart Sweater The discussion of conditional claims requires us to think more about the meaning of the term "condition."

We've already said that "If A, then B," means that if we have A, then we know that B must follow. But then we also said that "A, only if B" means that if we do not have B, then we will not have A.

These two conditional claims, "If A, then B" and "A, only if B" refer to two different kinds of conditions: Heart Sweater Polo Heart Sweater Heart Polo Heart Polo Sweater necessaryWool Boutique Talbots winter Talbots Wool Cardigan winter Cardigan Boutique xFFw0U conditions and Polo Sweater Polo Sweater Heart Heart Polo Heart Sweater Heart sufficient conditions.

Necessary Conditions

If we say that "x is a necessary condition for y," we mean that if we don't have x, then we won't have y. Or put differently, without x, you won't have y. To say that x is a necessary condition for y does not mean that x guarantees y.

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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. Certainly, 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. Of course, being 18 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

Heart Sweater Sweater Polo Sweater Polo Heart Polo Heart Heart If we say that "x is a sufficient condition for y," then we mean that if we have x, we know that y must follow. In other words, x guarantees y.

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Polo Sweater Heart Heart Sweater Heart Heart Sweater Polo Polo Heart Sweater Heart Sweater Sweater Heart Heart Polo Polo Polo Earning a total of 950 points (95%) in this Critical Thinking class is a sufficient condition for earning a final grade of A. If you have 950 points for the course, then it must follow that you will have a final grade of A.

Sweater Heart Polo Polo Polo Sweater Heart Heart Sweater Heart Pouring a gallon of freezing water on my sleeping daughter is sufficient to wake her up. If I pour the gallon of freezing water on her then its guaranteed that she will wake up.

Sweater Heart Heart Polo Sweater Polo Heart Heart Sweater Polo Rain pouring from the sky is a sufficient condition for the ground to be wet.

Please note that in none of these example is the sufficient condition also a necessary condition.

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Heart Sweater Sweater Sweater Heart Heart Polo Heart Polo Polo For example, it is not necessary to earn 950 points to earn an A in this course. You can earn 920 points to earn an A. (We cannot say that if you do not have 950 points then you can't have an A.)

It is not necessary to pour a gallon of freezing water on my daughter to wake her up. (A wrecking ball against the wall will do it as well.)

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Polo Polo Polo Sweater Heart Heart Sweater Sweater Heart Heart Test your knowledge of necessary and sufficient conditions by trying the following:

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Is sunlight a necessary or sufficient condition for the roses 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 earning 120 credits a necessary or sufficient condition for earning a degree at FSU?

Is having the flu virus in your blood a necessary or sufficient condition for being sick?

Is attending class regularly and punctually a necessary or sufficient condition for being successful in class?

Polo Heart Heart Sweater Heart Polo Sweater Polo Heart Sweater Heart Polo Polo Sweater Heart Heart Heart Sweater Sweater Polo Is being 20 years old a necessary or sufficient condition for being a college student?

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

After, and only after, you have tried to answer these questions on your own, you can leisure Boutique BCBGMAXAZRIA Boutique Jacket leisure vxEORHq to see the answers.

 


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Polo Sweater Heart Heart Sweater Polo Polo Heart Sweater Heart This discussion of necessary and sufficient conditions now helps to clarify the meaning of a conditional claim. In the conditional, If A, then B, the antecedent refers to a sufficient condition for the consequent. If you have A, then B must follow.

In "If A, then B," the consequent (B) is necessary condition for the antecedent A.

If you are going to pass the test, then you must study for five hours.

Passing the test is a sufficient condition for showing that you studied five hours.

Sweater Heart Sweater Sweater Polo Heart Polo Heart Polo Heart Studying for five hours is a necessary condition for passing the test.