By Howard Anton; Bernard Kolman

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Two ordered pairs are called equal if they list the same objects in the same order. Thus, for (a, b) and (c, d) to be equal ordered pairs, we must have a =c and b = d. We are now in a position to define the last set operation we shall need. 3 COMPLEMENTATION AND CARTESIAN PRODUCT OF SETS 25 If A and B are two sets, the set of all ordered pairs (a, b), where a EA and b E B, is called the Cartesiant product of A and B; it is denoted by the symbol AX B. Example 7 Let A and Then B { r, s, t} { 1 , 2, 3, 4} .

Thus, to sketch the graph we need only plot two points and draw the line through them. We will plot the inter sections with the coordinate axes. The line crosses the y axis where x = 0 and crosses the x axis where y = 0. Substituting x = 0 in the given equation and solving for y yields y = 2, so (0, 2) is the intersection with the y axis. Substituting y = 0 in the given equation and solving for x yields x = 8, so (8, 0) is the intersection with the x axis. The graph is shown in Figure 10. Linear equations may involve variables other than x and y.

25. 23-25 copy the Venn diagram in Figure (a) (a) A' u B (b) A' U B' (b) (a) (A ' U B)' (b) A' n B (c) (A U B)' (A ' u B')' (c) 10 and shade the indicated A ' n B' (A n B)' (c) (A ' n B')' In Exercises 26-27 copy the Venn diagram in Figure 1 1 and shade the indicated sets. (c) A n (B n C) (b) A n (B u C) 26. (a) A U (B n C) (c) A U (B U C')' 27. 3 COMPLEMENTATION AND CARTESIAN PRODUCT OF SETS 3 1 B c FIGURE 1 1 A prisoner can 28. escape from the penitentiary by digging a tunnel under the east wall , climbing over the west wall, or hiding in a laundry truck leaving the north gate.