Application of sufficient and necessary conditions
Introduction
In every field, there must be some form of application of sufficient and necessary conditions. The two terms are confusing to some extent, and some people may use them interchangeably. However, this should not be the case. Although the two conditions may be a relation to one particular subject, the two describe a totally different set of conditions. The two conditions describe the relationship between two related situations. It is widely applicable in the mathematical analysis where two variables are analyzed in relation to a particular subject. (Dul, J et al. 2010) Necessary and sufficient conditions relate to the importance of the condition in relation to the subject. Sufficient conditions are more critical than the necessary condition. In terms of definition, necessary conditions are a set of conditions that are required to be present for the given situation to happen. It is not a totality of the condition but rather some part of the required conditions. On the other hand, sufficient condition is a set of conditions in which, all the conditions required for a certain set of actions to take place are present. It signifies a totality in conditions required for a certain course of action. In other words, sufficient conditions can be argued to be perfection.
Taking an example in order to understand the two conditions better, for human beings, being a mammal, breathing, eating, walking are all necessary conditions for being a human being. This is because all human beings possess these attributes. It is a norm to see human beings breathe, eat, and walk. However, these conditions are not sufficient for being a human being. ( Dul, J et al. 2010)The characters are also available in other species, and therefore they alone cannot be used to define what a human being is. In order to develop a sufficient condition for being a human being, there are a set of conditions that can be used to define what a human being is. For instance, there is a unique characteristic in humans that can make them
- sufficient condition for being
from other mammals. For instance, a human being, in addition to what has already being said about mammals he or she can have the highest thinking capacity and makes some rational decisions that suppose those of other species.
There are conditions in which sufficiency and necessity mean the same thing, which means that each means the other. For instance, in the case where X is a necessary condition for y, this is translated to mean that it is impossible to have y without x. it is said that x causes y. it is, therefore, a necessary condition for the other. Absence of x results in the absence of Y. ( Dakić, B et al. 2010)the necessary condition is also known as an essential condition, meaning that without X there is no possibility of having Y without having the causative X. on the other hand, not all necessary condition is equal to the state they cause, in some cases, there are a set of many necessary conditions leading to a certain state. For instance, being a mammal, breathing, and walking is a set of conditions, necessary ones that are lead to a state of being a human being. However, this is only a necessary condition and not a sufficient one.
Necessity always causes sufficiency. Considering the examples below, where a four equal sides object is a necessary condition for a square. Therefore it means that you cannot argue that an object is a square if it doesn’t have four equal sides. It is, therefore, a sufficient condition meaning the square can be fully described as an object with equal sides. Not taking an example of a statement like ‘four sides object,’ this is a necessary condition for a square but not a sufficient one. Four sides object can even be used to mean a rectangle or a rhombus. Being Specific, therefore, helps reduce the ambiguity and lead to a sufficient condition as opposed to the more general statements. For instance, in our case concerning squares, lack of the word ‘equal’ changes the condition form sufficient into necessary.
Considering the following illustrations: indivisibility of a number by two is a sufficient condition for an odd number; being brave is also a sufficient condition for being a soldier, and lastly, a four equal side object is a sufficient condition for being a square. In the above illustration, X is a sufficient condition for Y, meaning that without the condition, the state cannot exist. However, another opposite set of condition provides the relationship between being rich, causing happiness. It is not proven that after becoming rich, somebody becomes happy (Xu, J., & Zhang, H. 2015). Therefore being rich may result in being happy, but it cannot do son independently. Therefore no one can argue that somebody is made happy solely by being rich. The same case applies in this other example, ‘Chinese are hog Kong, permanent residents.’ It is not a qualification for all the Chinese to be permanent Hong Kong residents. However, this is a necessary but not sufficient condition got being Chinese.
Sufficient conditions, on the other hand, the presence of X, guarantees the presence of y in any condition. Therefore it is impossible to have X without Y. In other words, X translates directly into Y, and therefore and its presence doesn’t require any combination with other conditions for it to cause y. it stands on its own, and therefore it is a singular causative element. Therefore when X is present in a condition, then it follows that Y is also present (Ma, C. Q., & Zhang, J. F. 2010). If, for instance, X is not a sufficient condition, we may come up with a situation where X is present, but Y is not. In this case, X won’t be a causative element of Y. for example, love is not a sufficient condition for being loved. It may happen that you love someone, but the reaction of that other person is not certain, they may choose to love back or not. Again Loyalty is not a sufficient condition for honesty. Someone might be loyal, but it may turn out to be honesty or dishonesty. These situations mean that X is not a perfect causative element of Y. in simple terms, X is not a sufficient condition for Y.
It should be noted that a certain state of affairs may have more than one sufficient condition. In such a state, then a number of statements may be referring to the same state. For instance, ‘if A then Y,’ ‘if B, then Y.’ It means that the state of affairs Y has two sufficient conditions A and B. for example, in mathematics, it is known that one plus one is equal to 2. This is one satisfying condition. On the other hand, two plus zero is equal to 2. The two sets of conditions, therefore, lead to the same state of affairs that is 2. Some states of the affair have multiple conditions, while others have only one set of conditions.
References
Dakić, B., Vedral, V., & Brukner, Č. (2010). Necessary and sufficient condition for nonzero quantum discord. Physical review letters, 105(19), 190502.
Dul, J., Hak, T., Goertz, G., & Voss, C. (2010). Necessary condition hypotheses in operations management. International Journal of Operations & Production Management.
Ma, C. Q., & Zhang, J. F. (2010). Necessary and sufficient conditions for the consensuality of linear multi-agent systems. IEEE Transactions on Automatic Control, 55(5), 1263-1268.
Xu, J., & Zhang, H. (2015). Sufficient and necessary open-loop Stackelberg strategy for the two-player game with time delay. IEEE transactions on cybernetics, 46(2), 438-449.