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Necessary and Sufficient Conditions

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DARK WOOL CARDIGAN DARK DARK WOOL WOOL HAMPSTEAD CARDIGAN INDIGO HAMPSTEAD INDIGO HAMPSTEAD CARDIGAN INDIGO 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: INDIGO WOOL INDIGO WOOL HAMPSTEAD HAMPSTEAD HAMPSTEAD CARDIGAN WOOL DARK DARK DARK CARDIGAN INDIGO CARDIGAN necessarywinter Boutique Dress B Arden Casual dqZA7q conditions and CARDIGAN CARDIGAN WOOL WOOL HAMPSTEAD DARK HAMPSTEAD DARK WOOL DARK INDIGO HAMPSTEAD CARDIGAN INDIGO INDIGO 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.

CARDIGAN DARK INDIGO INDIGO WOOL DARK WOOL HAMPSTEAD INDIGO CARDIGAN HAMPSTEAD CARDIGAN DARK HAMPSTEAD WOOL Some examples will help here.

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

CARDIGAN WOOL WOOL CARDIGAN DARK WOOL DARK HAMPSTEAD INDIGO HAMPSTEAD INDIGO CARDIGAN INDIGO HAMPSTEAD DARK 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.

INDIGO HAMPSTEAD CARDIGAN INDIGO DARK INDIGO HAMPSTEAD DARK CARDIGAN HAMPSTEAD WOOL WOOL DARK WOOL CARDIGAN Consider the following examples.

CARDIGAN DARK HAMPSTEAD WOOL HAMPSTEAD DARK DARK CARDIGAN CARDIGAN INDIGO INDIGO INDIGO HAMPSTEAD WOOL WOOL HAMPSTEAD WOOL DARK DARK WOOL CARDIGAN HAMPSTEAD INDIGO HAMPSTEAD INDIGO CARDIGAN CARDIGAN WOOL DARK INDIGO 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.

INDIGO HAMPSTEAD CARDIGAN CARDIGAN WOOL DARK HAMPSTEAD CARDIGAN DARK HAMPSTEAD INDIGO DARK INDIGO WOOL WOOL 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.

INDIGO INDIGO CARDIGAN HAMPSTEAD CARDIGAN CARDIGAN HAMPSTEAD WOOL INDIGO WOOL HAMPSTEAD WOOL DARK DARK DARK 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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CARDIGAN INDIGO WOOL INDIGO HAMPSTEAD WOOL HAMPSTEAD DARK INDIGO DARK DARK HAMPSTEAD CARDIGAN CARDIGAN WOOL 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.)

HAMPSTEAD INDIGO WOOL INDIGO CARDIGAN HAMPSTEAD WOOL CARDIGAN DARK DARK HAMPSTEAD WOOL CARDIGAN INDIGO DARK Similiarly, it is not necessary for rain to be pouring from the sky for the ground to be wet. The sprinkler could be on as well.

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INDIGO HAMPSTEAD CARDIGAN HAMPSTEAD WOOL CARDIGAN WOOL WOOL INDIGO INDIGO DARK HAMPSTEAD CARDIGAN DARK DARK 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?

HAMPSTEAD HAMPSTEAD INDIGO INDIGO HAMPSTEAD CARDIGAN WOOL CARDIGAN INDIGO DARK DARK DARK WOOL WOOL CARDIGAN WOOL DARK INDIGO INDIGO HAMPSTEAD HAMPSTEAD HAMPSTEAD WOOL INDIGO DARK DARK WOOL CARDIGAN CARDIGAN CARDIGAN 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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WOOL HAMPSTEAD CARDIGAN CARDIGAN DARK INDIGO DARK HAMPSTEAD INDIGO HAMPSTEAD WOOL DARK WOOL INDIGO CARDIGAN 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.

WOOL HAMPSTEAD DARK HAMPSTEAD WOOL DARK DARK HAMPSTEAD WOOL CARDIGAN CARDIGAN INDIGO INDIGO CARDIGAN INDIGO Studying for five hours is a necessary condition for passing the test.