Sufficient & Necessary Forum

[e10]

Can someone please clarify and provide an example, please?

I am not sure which is correct, if there is a sufficient condition it means there is a necessary or can a sufficient stand alone and if you have a necessary conidition it means that there is a sufficient condition or a necessary can stand alone?

[StrictlyLiable]

Necessary is necessary. The answer can be found by negating the right answer, which will destroy the argument. I am a little confused by your question.

[Anaconda]

When a sufficient event occurs, the necessary event must occur. When a necessary event occurs, the sufficient event may or may not happen.

Ex: If I eat a Big Mac then I will be full.

Suff condition: I eat a Big Mac
Nec condition: I will get full.

Eating a Big Mac is sufficient to get full. If you eat a Big Mac you WILL get full.

However, just because you get full does not mean you ate a Big Mac. You could have eaten pizza, a sandwich, or other things. A Big Mac isn't a necessary condition for being full, it's only sufficient. However, if you are full it could also mean you ate a Big Mac.

Does that make sense?

[vanwinkle]

Necessary: You must have the condition for the statement to be true.
Sufficient: This particular condition makes the statement true, though it's not necessarily the only condition that could do so.

Examples:

(Assume for the example your car doesn't need premium fuel.)

It is necessary to have gasoline in your car for it to run.
It is sufficient to have premium fuel in your car for it to run.

Having premium fuel in the car allows it to run, but it's not necessary, there are other things that can also fulfill the condition. If you do not have premium fuel, it's still possible to get the car to run (you just need a different kind of gasoline). It's sufficient, but it's not necessary.

However, some kind of gasoline is required. Gasoline in some form is necessary. If you do not have gasoline, the car will not run.

[AverageTutoring]

Can someone please clarify and provide an example, please?

I am not sure which is correct, if there is a sufficient condition it means there is a necessary or can a sufficient stand alone and if you have a necessary conidition it means that there is a sufficient condition or a necessary can stand alone?

A necessary condition is one that is required for a certain result to happen. For example, it is necessary for a regular Law School applicant to have a steller LSAT to gain admission into top law schools. In real life terms this means if you get into the T14 or HYS (as a regular applicant) you MUST have a great LSAT score.

Diagramming this out,

Accepted at some schools in the T14 (as a regular applicant) --> Applicant had a stellar LSAT

However, just because you have a stellar LSAT DOES NOT MEAN you will be accepted into the T14. If your grades are sub-par, for example, schools might not accept you. So while it is necessary for an applicant to have a stellar LSAT to be accepted, this by itself, it not sufficient to gaurentee admission.

A sufficient condition is one that will absolutely bring about a certain result. For example, if I don't pay my bills, my electricity will be cut off. In this example, by not paying my bills I am guaranteeing (or otherwise am completing an action otherwise sufficient for) my electricity to be cut off.

So while a necessary condition is something that is required for a result to happen, a sufficient condition is one that is guaranteed to bring about that result.

In terms of conditional statements:

Sufficient Condition --> Necessary Condition

Sufficient is on the left and Necessary is on the right.

[3|ink]

Can someone please clarify and provide an example, please?

I am not sure which is correct, if there is a sufficient condition it means there is a necessary or can a sufficient stand alone and if you have a necessary conidition it means that there is a sufficient condition or a necessary can stand alone?

To answer your question as frankly as possible, no. Within the confines of a conditional statement, you can't have a necessary condition without a sufficient condition or vice versa. This is because sufficient and necessary conditions are relative to one another. When we refer to a sufficient, we're referring to the condition that guarantees a necessary condition. When we refer to a necessary condition, we're referring to the condition that must be present in order for the sufficient condition to be present.

The reason for this is simple. You can only have a sufficient/necessary relationship with a conditional statement. The definition of a condition statement for the purpose of the LSAT is a statement that describes the relationship of two conditions (that's a rough definition).

In summary, the reason that you can't have a stand-alone sufficient or necessary condition is that one exists to describe its relationship to the other.


Example:

Conditional
A ---> B

Translation:
"If condition 'A' is present, then condition 'B' must be present.

Stand Alone
A
Translation:
'A' exists.

Edited a bunch for clarity.

[ArchRoark]

To answer your question as frankly as possible, no. You can't have a necessary condition without a sufficient condition or vice versa.

Huh? Necessary conditions can stand by themselves.

If Nikki is at the party, Bill will be there to.

Taken this statement.

Sufficient--->Necessary
Nikki--->Bill

Now if bill is at the party (which is entirely reasonable/possible) that does not mean that Nikki is there.

The options are...
1) Nikki and Bill are both at the party.
2) Bill is at the party alone.
3) Neither Nikki nor Bill are at the party.

While the following is entirely nitpicky... it is not a causal relationship. The sufficient doesn't have to cause the necessary to occur (although it can). The necessary condition can come before or at the same time or after the sufficient occurs. The sufficient just states that the necessary must take place without implying a chronological constraint.

EDIT: I think I misinterpreted your statement. I see what you mean that a necessary condition is only such by the nature of its relationship to its partnered sufficient condition.

[3|ink]

Huh? Necessary condition can stand by themselves.

If Nikki is at the party Bill is there to.

Taken this statement.

Sufficient--->Necessary
Nikki--->Bill

Now if bill is at the party (which is entirely reasonable/possible) that does not mean that Nikki is there.

The options are...
1) Nikki and Bill are both at the party.
2) Bill is at the party alone.
3) Neither Nikki nor Bill are at the party.

A necessary condition can occur by itself. However, you can't have a conditional statement without both necessary and sufficient conditions. That was the point I was trying to make.

OP - Sorry if I made it more confusing. In the context of a conditional statement, you must have both a necessary and a sufficient condition. However, if you have a statement of fact (such as that which was presented in my example A), then it may be possible to deduce the existence of the other conditions.

[dakatz]

Huh? Necessary condition can stand by themselves.

If Nikki is at the party Bill is there to.

Taken this statement.

Sufficient--->Necessary
Nikki--->Bill

Now if bill is at the party (which is entirely reasonable/possible) that does not mean that Nikki is there.

The options are...
1) Nikki and Bill are both at the party.
2) Bill is at the party alone.
3) Neither Nikki nor Bill are at the party.

A necessary condition can occur by itself. However, you can't have a conditional statement without both necessary and sufficient conditions. That was the point I was trying to make.

I had a feeling that this is what you were trying to say.

[ArchRoark]

A necessary condition can occur by itself. However, you can't have a conditional statement without both necessary and sufficient conditions. That was the point I was trying to make.

Beat me to my ninja edit. Yup yup we are in agreement.

[Anaconda]

We should have a contest - the OP will determine which explanation was most helpful, haha.