Pure Mathematics

# Download Applied Finite Mathematics by Howard Anton and Bernard Kolman (Auth.) PDF By Howard Anton and Bernard Kolman (Auth.)

Lifelike and suitable functions from various disciplines aid encourage enterprise and social technology scholars taking a finite arithmetic direction. a versatile supplier permits teachers to tailor the e-book to their direction

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Example text

Thus if Pi(xi, yi) and Ρ 2 (ζ 2 , 2/2) arc points on L, we must have y2 = y\. Therefore m = 0 from Equation (1). 10 x*y2 All points on L have equal y coordinates. 11 The slope of a line has a useful physical interpretation. Imagine a particle moving rightward along a line L from a point Pi(x h y{) to a point P 2 (%, 2/2). 11, the particle moves y2 — V\ units in the y direction as it travels x2 — X\ units in the x direction. From (1) these quantities are related by 2/2 - y\ = m(x2 - zi), (2) where m is the slope of the line.

Solution (b) The members of A n B' Π C" belong to A but not to 5 and not to C. 19. There are a number of useful properties of the complementation opera­ tion. We shall discuss a few of the more important ones here. We begin with the following two important results, called DeMorgan'sf laws. 19 t Augustus DeMorgan (1806-1871), British mathematician and logician—DeMorgan, the son of a British army officer, was born in Madura, India. He graduated from Trinity College in Cambridge, England in 1827, but was denied a teaching position there for refusing to subscribe to religious tests.

A) (Af)'= A (b) AUA'=U (e) A fi A ' = 0 . 23. 23 *w 3 0 / 1 : SET THEORY 15. In each case determine which of the points x, y, z, w belong to the indicated set. (a) c't\B' (c) i n s ' n c 16. 17. 18. (b) An#nc" (d) i ' n s ' n c . Follow the directions of Exercise 15 for the sets (a) A'VB (b) J5'UC" (c) A ' U t f ' U C " (d) A'UBUC'. In each part, find the values of x and y for which the given ordered pairs of integers are equal. (a) (*,7) = (3,7) (b) (2z,3) = (6,*/) (c) (4, y + 7) = (2s + 2, 14) (d) (x2, 9) = (16, 9 ) .