By Howard Anton; Bernard Kolman

Life like and appropriate purposes from a number of disciplines support inspire enterprise and social technological know-how scholars taking a finite arithmetic path. a versatile company permits teachers to tailor the publication to their direction

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Describe the following set� (a) A' (b) B' (c) (A U B) ' (d) (A n B)'. 4. Let U = the set of all real numbers A = { x I x is a solution of x2 = 1 } B = l - 1 , 2). Find (a) A' (b) B' (c) (A U B) ' (d) ( A n B) '. 5 . Let A = I x J x is an integer satisfying x > 0 } . Specify a universal set and compute A'. 6. S. senators. Specify a universal set and compute D'. 3 COMPLEMENTATION AND CARTESIAN PRODUCT OF SETS / 29 7. Let C be the set of all consonants in the English alphabet. Specify a universal set and compute C'.

For this reason, m is said to measure the rate at which y changes with x along the line L. Example 9 In Example 7, we showed that the line determined by the points P1(4, 1) and P2(6, 9) has slope m = 4. 12 ) . 12 x 54 / 2: COORDINATE SYSTEMS AND GRAPHS It was also shown in Example 7 that the line determined by the points P1 (1, 1 1 ) and P2(4, 5) has slope m = - 2. 13 ) . 14 we have sketched several lines with varying slopes. Observe that lines with positive slope are inclined upward to the right, while lines with negative slope are inclined downward to the right.

Solution (b) The members of A n B' n C' belong to A but not to B and not to C. 19. There arc 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' st 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.