which of the following is sufficent condition foe two different function to Be equal
Answers
Step-by-step explanation:
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If P then Q", Q is necessary for P, because the truth of P guarantees the truth of Q (equivalently, it is impossible to have P without Q).[1][2] Similarly, P is sufficient for Q, because P being true always implies that Q is true, but P not being true does not always imply that Q is not true.[3]
In general, a necessary condition is one which must be present in order for another condition to occur, while a sufficient condition is one which produces the said condition.[4] 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.[5] That is, the two statements must be either simultaneously true, or simultaneously false.[6][7][8]
In ordinary English, "necessary" and "sufficient" indicate relations between conditions or states of affairs, not statements. For example, being a male is a necessary condition for being a brother, but it is not sufficient—while being a male sibling is a necessary and sufficient condition for being a brother.
Mathematics Magazine presents articles and notes on undergraduate mathematical topics in a lively expository style that appeals to students and faculty throughout the undergraduate years. The journal originally began in 1926 as a series of pamphlets to encourage membership in the Louisiana-Mississipi Section of the Mathematical Association of America, and soon evolved into the regional publication Mathematics News Letter. Beginning in 1935, the journal was published with the help of Louisiana State University and, as it began addressing larger issues in teaching math, was renamed National Mathematics Magazine. In 1947, the journal's title was shortened to Mathematics Magazine, and in 1960 it became an official publication of the Mathematical Association of America. Mathematics Magazine is published five times per year.