definition of the algebraic properties of set operations

Binary Operations - Binary Operations are as given below, Commutative Law Associative Law Let S be any non-empty set. An operation * is called a binary operation on S if " a, b Î S a * b Î SLet S be any non-empty set. An h..

binary operation: Let S be any non-empty set. An operation * is called a binary operation on S if " a, b S a * b S Commutative law: Let * be a binary operation on the set S. * is said to be associative in S if " a..

Consider the set A = {a, b, c, } then any subset of A x A is called a relation in A. Let R be any relation in A so that R is a subset of the product set A x A. We will discuss the properties a relation may possess.Consider the set A = {a, b, c, } then any sub..

Reflexive property: A relation R in a set A is said to be reflexive if every element of the set A is related to itself. This is if aRa where a A, or (a, a) R for each a A. Transitive property: A relation R, is said to be transitive if..

Summary of Relation properties - (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 a..

(1) '+' is a binary operation on the set of naturals. (2) '.' is a binary operation on the set of naturals. (iv) Addition, subtraction and multiplication are binary operations on ..

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 is call..

A pair of objects, written in a specified order is called an ordered pair . A pair of objects, written in a specified order is called an ordered pair . For the ordered pair (a,b), a is called the first element and b, the second element. The ordered pairs (a,b) and (c,d) are equal if th..

The following are the Operation on Real Functions: Sum Function, Difference Function, Product Function, Quotient Function, Scalar Multiplication Function, Composite Functions, Inverse Function..

A relation R, is said to be transitive if a 'is related to' b and b 'is related to' c then a 'is related to' c, (a, b) R and if aRb, bRc then aRc. For example, (i) If D ABC 'is congruent to' D DEF and D DEF 'is congruent to' D XYZ, then D ABC 'is congruent to' D X..