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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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 ) .