## Difference Between Necessary and Sufficient

**Necessary vs. sufficient**

How do we know that a certain statement is true? There are two ways in determining that a statement is true. This is through using the necessary or sufficient method. Necessary and sufficient implies that a statement is true either because of the former statement or the latter statement. One must be proven for a certain statement to be true while the other must follow a certain requirement for it to be true. Necessary and sufficient are two different ways in proving that a statement is true. As you read further on you might get confused with the essence of necessary and sufficient, but as you will frown upon it you will notice how everything that this article will say makes sense.

Here are the differences between the two. A condition which is necessary tells that a statement should be proven for it to be true while a condition which is sufficient is a statement that, if proven, can be guaranteed to be true. An example of a necessary condition is ‘you are my little brother.’ You must be younger, a male and must be related to that person who is saying the statement for the statement ‘you are my little brother’ to be true. That is a necessary condition. To make it a sufficient condition, knowing that you are younger, you are a male and you are related to the person saying the statement means that ‘you are my little brother’ is true.

This means a necessary condition, considering P, P is a necessary of Q, if Q indicates P. This will be stated as, P is a necessary of Q. This means Q must be true so that P will also be true. And Q will be false, if ever P is false. For example, you must be 18 to serve in the army, if you are not yet 18 then you can’t serve in the Army, which also means if you are in the army, it means you are 18 years old or above.

A sufficient condition on the other hand shows that if P is true then Q is guaranteed to be true. This means P being true is enough for Q to also be true. An example for this is, being a singer is sufficient for having a great voice. This means if you are a singer, it follows that you have a great voice.

There are also some instances where P is necessary and sufficient to Q. Sometimes there are things that are easily proven or are already guaranteed or are already given to be true (which makes it a condition both necessary and sufficient). By using the necessary and sufficient conditions, it will be easier to prove statements.

Summary:

1.

The former statement must be true for a statement to be true in a sufficient condition and later for the necessary condition.

2.

A necessary condition should be proven by the next statement while a sufficient condition, if proven true, the next statement follows to be true as well.

3.

P is a necessary of Q if Q indicates P, while P is a sufficient of Q if, If P is true then Q is guaranteed to be true.

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