relations and functions summary

from a set A to a set B is a subset of A x B. - A relation R on a set A is reflexive if a R a, " a A- A relation R on a set A is symmetric if a R b b R a. - A relation R on a set A transitive if a R b and b R c a R c. A relation R is said to be an equivalence..

Summary - Cell is the structural and functional unit of the organism. Water is the principal constituent of plants and is essential for the maintenance of life, growth and development. Plants absorb water from the soil through their roots, transport it to other parts of the plan..

A function is a relation on A x B is which A function is a relation on A x B is which (i) no two second elements have a common first element. (ii) every first element has a corresponding second element. Every function is either one-one onto or..

>The homeostatic mechanisms work on a negative feedback. In order to ensure the continuation of species, all living organisms exhibit reproduction. The entire cellular information is stored in the DNA which undergoes replication to transfer the information to the successive generations. The surviva..

. The nervous system has three parts - central nervous system (CNS), peripheral nervous system (PNS) and autonomic nervous system (ANS). The CNS is made up of brain and spinal cord. Brain has different areas that are responsible for specific functions. The areas are divided into: - sensor..

> = -1 the curves are orthogonal. The condition for the function f(x) to be increasing at x = a if f ' (a) >0. The condition for f(x) to be decreasing at x = a if f ' (a) < 0. A function f(x) is said to be strictly increasing at x = a if f(x) > f(a) whenever x > a in..

A relation becomes a function only if _______. => for two inputs there is exactly one output or for every input, there are fixed number of outputs or for every input there are two outputs or for every input there is exactly one output..

In our daily life, we come across many relations such as father-son, brother-sister, teacher-student and many more. In mathematics too, we come across relations such as . A is a subset of B . line l is parallel to line m . number m is less than number n . In ..

(i) R is reflexive if aRa (ii) R is transitive if aRb and bRc implies aRc(i) R is reflexive if aRa (ii) R is transitive if aRb and bRc implies aRc (iii) R is symmetric if aRb implies bRa. A relation which is reflexive, transitive, and symmetric is called an equivalence relation..

Molecular mass is the average relative mass of a molecule of the substance as compared with mass of an atom of carbon (C-12) taken as 12 a.m...