algebraic operations in mathematics

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 operation *..

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, b S a * b = b ..

(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 ..

Let * be a binary operation on the set S. * is said to be associative in S if " a, b S a * b = b ..

Summary - In a given sentence, the variables are replaced by letters and the different operations are replaced by their mathematical symbols. We now arrive at a formula. In a given sentence, the variables are replaced by letters and the different operations are replace..

Summary Relations and Functions - 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 ..

If f and g are two functions defined over same domain D, then we have certain set of identities which can be used for solving limits problems with variables like algebraic expression..

The product of a + b and a 2 - ab + b 2 is a 3 + b 3 . Hence when a 3 + b 3 is factorised, we get: a 3 + b 3 = (a + b) (a 2 - ab + b 2 ) Similarly, a 3 - b 3 = (a - b) (a 2 + ab + b 2 ) Factorise: x 3 + 8 x 3 + 8 = (x) 3 + (2) 3 = (x + 2) (x 2 - 2x + 4) Factorise 64x 3 - 125. ..

A formula is formed by using: (a) mathematical symbols and variables (b) given conditions, and (c) simplificatio..

We use alphabets like x, y, z etc., to denote variables. For example the length of a rectangle is denoted by 'l'. It takes different values in different rectangles. A formula is a relation between different variables formed using mathematical symbols. Any given condition can be translat..