**Necessary and Sufficient Conditions**

**Speed Short Speed Short Speed Short Short Speed Short Short Speed Speed Speed Short Speed Short** 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: **Short Short Speed Speed Short Short Speed Short Speed Short Speed Short Short Speed Speed Speed necessary**Khaki Crew leisure Boutique J Shorts awT4zFq conditions and ** Speed Short Short Speed Speed Short Speed Speed Speed Short Short Short Speed Short Speed Short 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.

**Speed Short Speed Speed Short Speed Speed Speed Short Speed Short Speed Short Short Short Short** 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**

**Speed Speed Short Short Speed Speed Short Speed Speed Short Short Short Speed Short Short Speed** 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.

**Short Short Speed Short Short Speed Short Speed Short Speed Short Speed Speed Speed Short Speed** Consider the following examples.

*Speed Short Short Speed Short Speed Speed Short Speed Short Speed Short Speed Short Speed Short* Speed Short Speed Short Speed Short Speed Short Short Short Speed Speed Speed Speed Short Short 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.

**Short Short Short Speed Speed Short Short Speed Short Speed Speed Short Speed Short Speed Speed** 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.

**Speed Short Speed Speed Speed Speed Short Speed Short Short Short Speed Short Short Short Speed** 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.

**Short Short Speed Speed Short Speed Speed Short Speed Short Short Speed Speed Short Short Speed** 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.)

*Speed Speed Short Short Short Speed Short Speed Speed Speed Speed Short Short Speed Short Short* 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.

**Speed Speed Short Short Speed Speed Speed Short Speed Short Short Short Short Speed Speed Short Test your knowledge of necessary and sufficient conditions by trying the following:**

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?

Speed Speed Speed Speed Short Short Short Short Short Speed Speed Short Speed Short Speed Short **Short Short Speed Speed Short Speed Short Short Speed Short Speed Short Speed Short Speed Speed** 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?

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Short Short Short Speed Short Short Speed Speed Speed Short Speed Speed Short Short Speed Speed 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.

*Speed Short Speed Short Short Speed Speed Speed Short Speed Short Short Short Speed Speed Short* Studying for five hours is a necessary condition for passing the test.