How do you prove necessary and sufficient conditions?
The assertion that a statement is a ” necessary and sufficient ” condition of another means that the former statement is true if and only if the latter is true. That is, the two statements must be either simultaneously true, or simultaneously false.
What is the necessary and sufficient condition for stability?
A necessary and sufficient condition for stability of a perturbed system. Abstract: The problem of determining the stability of a feedback system in the presence of perturbation is considered. A necessary and sufficient condition under which the perturbed system remains stable is obtained.
What are the necessary conditions for a group explain?
In mathematics, a group is a set equipped with a binary operation that combines any two elements to form a third element in such a way that four conditions called group axioms are satisfied, namely closure, associativity, identity and invertibility.
What is necessary condition in economics?
Necessary Condition Suppose that A and B are statements. We say that the statement A is necessary for the statement B if B cannot be true unless A is also true. In other words, B requires A. However it is possible for A to be true even if B is not true.
Is a sufficient condition?
A sufficient condition is a condition or set of conditions that will produce the event. A necessary condition must be there, but it alone does not provide sufficient cause for the occurrence of the event. Only the sufficient grounds can do this. In other words, all of the necessary elements must be there.
Can something be sufficient but not necessary?
A sufficient condition guarantees the truth of another condition, but is not necessary for that other condition to happen. A necessary condition is required for something else to happen, but it does not guarantee that the something else happens.
What is the condition for stability?
A system is said to be stable , if its output is under control. Otherwise, it is said to be unstable. A stable system produces a bounded output for a given bounded input. The following figure shows the response of a stable system.
What is the necessary condition for stability?
Necessary Condition for Routh-Hurwitz Stability The necessary condition is that the coefficients of the characteristic polynomial should be positive. This implies that all the roots of the characteristic equation should have negative real parts.
What is the stability?
1 : the quality, state, or degree of being stable : such as. a : the strength to stand or endure : firmness. b : the property of a body that causes it when disturbed from a condition of equilibrium or steady motion to develop forces or moments that restore the original condition.
What is the difference between necessary and sufficient cause?
If A is necessary for B ( necessary cause ) that means you will never have B if you don’t have A. If A is sufficient for B ( sufficient cause ), that means that if you have A, you will ALWAYS have B. In other words, if something is a sufficient cause , then every time it happens the outcome will follow.
What does jointly sufficient mean?
Frequently the terminology of “individually necessary” and ” jointly sufficient ” is used. One might say, for example, “each of the members of the foregoing set is individually necessary and, taken all together, they are jointly sufficient for x’s being a square.”
Is having four legs sufficient for being a chair is it necessary explain?
Chairs do not need to have four legs . They can have three legs , two legs even one leg or no legs at all. Chairs do not nee to be made of wood or metal .
Is only if sufficient or necessary?
It’s important to remember that ” only ,” ” only if ,” and ” only when ” all introduce the necessary condition. These ” necessary condition prompters” should not be clumped together with the notorious “the only .” “The only ” will introduce the sufficient condition.
How do we typically define necessary?
1 : absolutely needed : required Food is necessary for life. 2a : of an inevitable nature : inescapable Death is a necessary feature of the human condition. b(1) : logically unavoidable a necessary conclusion. (2) : that cannot be denied without contradiction.
What is the meaning of necessary?
adjective. being essential , indispensable, or requisite: a necessary part of the motor. happening or existing by necessity: a necessary change in our plans. acting or proceeding from compulsion or necessity; not free; involuntary: a necessary agent.