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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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.

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