By Howard Anton and Bernard Kolman (Auth.)

Lifelike and proper functions from quite a few disciplines aid inspire company and social technology scholars taking a finite arithmetic direction. a versatile organization permits teachers to tailor the publication to their path

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**Finite Mathematics: An Applied Approach, 11th Edition **

Now in its 11th version, this article once more lives as much as its acceptance as a in actual fact written, entire finite arithmetic ebook. The 11th version of Finite arithmetic builds upon an excellent origin via integrating new positive factors and methods that extra increase scholar curiosity and involvement.

**Study Guide for Applied Finite Mathematics**

Practical and appropriate functions from quite a few disciplines support encourage enterprise and social technology scholars taking a finite arithmetic direction. a versatile organization permits teachers to tailor the booklet to their path

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4 COUNTING ELEMENTS IN SETS Suppose we know the number of elements in a set A and the number of elements in a set B. What can we say about the number of elements in A UB and A X 5 ? In this section we investigate problems like these and illustrate some of their applications. If S is a set with a finite number of elements, then we shall denote the number of elements in S by the symbol n(S). Example 34 Consider the sets A = [a, e, 0,1} B = {x | x is a positive integer} C = 0. Since A has four elements, we have n(A) = 4.

A point with two positive coordinates ( + , + ) lies in Quadrant I, a point with a negative x coordinate and a positive y coordinate ( —, + ) lies in Quadrant II, and so on. Cartesian coordinate systems are helpful for giving a geometric descrip tion of equations involving two variables. To explain how, we shall need some preliminary ideas. We shall assume in our discussion that a Cartesian coordinate system has been constructed and that we are given an equa tion involving only two variables, x and 2/, such as Sx + Sy = 4, x2 + y2 = 1, or y = Given an equation involving only the variables x and y, we call an ordered pair of real numbers (a, b) a solution of the equation if the equation is satisfied when we substitute y = b.

To explain how, we shall need some preliminary ideas. We shall assume in our discussion that a Cartesian coordinate system has been constructed and that we are given an equa tion involving only two variables, x and 2/, such as Sx + Sy = 4, x2 + y2 = 1, or y = Given an equation involving only the variables x and y, we call an ordered pair of real numbers (a, b) a solution of the equation if the equation is satisfied when we substitute y = b. x = o, Example 3 The ordered pair (4,5) is a solution of the equation Sx - 2y = 2 since the equation is satisfied when we substitute x = 4, y = 5.