equivalence relations in relations

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..

Relatives - The words who, which, where and whose are called relatives which give us information about a person or thing and help us to convey two-different ideas in a well-connected wa..

A relation R is a non-empty sub-set of a cartesian product. A relation R is a non-empty sub-set of a cartesian product. A relation is a set of ordered pairs, i.e., R A x B where A and B are two non-empty sets. If R is a relation, write x R y or (x, ..

The words who, which, where and whose are called relatives which give us information about a person or thing and help us to convey two-different ideas in a well-connected wa..

If A and B are two non-empty sets, then a relation R in A x B is a subset of A x B. If we use the letter R to denote a relation, then we can write the relation between a and b as aRb a is related to b. Let R mean 'is greater than', then xRy means x > ..

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..

subset of is an antisymmetric relation. On the set of integers, the relation congruence is an equivalence relatio..

> 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 ..

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 ..