Discrete Mathematics with Graph Theory (3rd Edition) 241

# Discrete Mathematics with Graph Theory (3rd Edition) 241 -...

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Section 8.4 239 5. 6. (b) Recall from (a) that all numbers to the left of x = 7rj are the same in 7r and 7r' and hence in a. Also, since x is replaced (in 7r') by the smallest number m to its right which is greater than x, and the sequence of numbers following m is strictly increasing in 7r', it follows that x must also be in the same position in a as in 7r. But, since the sequence of integers following x in 7r is strictly decreasing and since 7r ::S a, it can only be that 7r = a. (a) [BB] 1234 1235 1236 1245 1246 (b) 123 124 125 126 134 1256 1345 1346 1356 1456 135 136 145 146 156 2345 2346 2356 2456 3456 234 235 236 245 246 256 345 346 356 456 (a) [BB] 23459, 23467, 23468 precede; 23478, 23479, 23489 follow. (b) 13478, 13479, 13489 precede; 13568, 13569, 13578 follow. (c) 45678,45679,45689 precede; 46789 and 56789, the last combination in the list, follow. 7. (a) 12 13 14 15 16 17 23 24 25 26 27 34 35 36 37 45 46 47 56 57 67 8. (b) [BB] First list the combinations of 1, 2,
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