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SS 1 Further Mathematics (1st Term)

Further Maths

BINARY OPERATIONS: IDENTITY AND INVERSE ELEMENTS

BINARY OPERATIONS: IDENTITY AND INVERSE ELEMENTS Identity element and Inverse element CONTENT: Identity Element: Given a non- empty set S which is closed under a binary operation * and if there exists an element e € S such that a*e = e*a = a for all a € S, then e is called the IDENTITY or NEUTRAL element. The element is unique. Example: The operation * on the set R of real numbers is defined by a*b = 2a-1 ┼ b 2 for all a, b € R. Determine the identity element. Solution: a*e= e*a = a a*b= 2a-1 ┼ b 2 a*e = 2a-1 ┼ e = a 2 2a-1+ 2e = 2a 2e = 2a-2a +1 e   = ½.   Evaluation Find the identity element of the binary operation a*b = a +b+ab Inverse Element; If x € S and an element x-1 € S such that x*x-1… Read More »BINARY OPERATIONS: IDENTITY AND INVERSE ELEMENTS

Further Maths

BINARY OPERATIONS: BASIC CONCEPT OF BINARY OPEATIONS

BINARY OPERATIONS: BASIC CONCEPT OF BINARY OPEATIONS CONTENT Concept of binary operations, Closure property Commutative property Associative property and Distributive property. Definition Binary operation is any rule of combination of any two elements of a given non empty set. The rule of combination of two elements of a set may give rise to another element which may or not belong to the set under consideration. It is usually denoted by symbols such as, *, Ө e.t.c.   Properties: Closure property:  A non- empty set z is closed under a binary operation * if for all a, b € Z. Example; A binary operation * is defined on the set S= {0, 1, 2, 3, 4} by X*Y = x + y –xy. Find (a) 2 * 4 (b) 3* 1 (c) 0* 3.  Is the set S closed under the operation *? Solution 2 * 4, i.e, x= 2,y=4 2+… Read More »BINARY OPERATIONS: BASIC CONCEPT OF BINARY OPEATIONS

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