equivalence relation

If a relation is (i) reflexive, (ii) transitive and, (iii) symmetric, then it is called an equivalence relation. For example, (i) is congruent to (ii) is parallel to (iii) is similar to, are some examples of equivalence relations..

Ordered Pairs - An ordered pair has a pair of elements which occur in a definite order.An ordered pair has a pair of elements which occur in a definite order. Take two numbers 3 and 5. If they form a pair (3,5) and the order of the numbers cannot be changed, these numbers are said to form an ordere..

> and 'c' are constants, c 2 . 2m dm - m 2 . 2v dv - v 2 . 2m dm = 0 c 2 dm = mv . dv + v 2 dm = dK [from equation (i)] dK = dm . c 2 If particle is accelerated from rest to a velocity v, let its mass m 0 increase to m. K = (m - m 0 ) c 2 K + m 0 c 2 = mc 2 Here, the quantity m 0 c 2 is the energy ..

In 1 cm 3 of the solution containing 1 gm eq. of the electrolyte is taken in the vessel. The conductance of the solution will be equal to the specific conductivity and the equivalent conductivit..

Following are the types of relations: Reflexive Relation, Symmetric Relation, Transitive Relation, Equivalence Relation..

Summary Ordered Pairs and Cartesian Product - An ordered pair has a pair of elements which occur in a definite order. An ordered pair has a pair of elements which occur in a definite order. Cartesian Product - Given two sets A and B, all possible ordered pairs (x, y) obtained such that x A and y B ..

(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 re..

It is defined as the conductance of that volume of solution which has one equivalent dissolved in it. V = Volume of solution which has one equivalent in it. N normality (Number of equivalents per liter or 1000c..

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 equiva..

Einstein derived a formula given the relation between mass and energy as E = mc 2 . Here 'm' is the mass, 'c' is the velocity of light and 'E' is the energy. This equation has given equal states to mass and energy. It states that a mass m has energy E given by the above formula. Since the..