76
Solutions to Exercises
(c) By the result of part (a), 319
566
has 1+ LloglO 319
566
J
digits. Since 10glO 319
566
=
566 log
10
319
~
1417.15, the integer 319
566
has 1418 digits.
Exercises
4.2
1. (a) [BB] Not totally ordered; for example, 6 and 21 are not comparable.
(b) [BB]
1
is a minimum element since
1 1
n
for all
n
E N,
but there is no maximum element since
given any
n
E N,
n
1
2n,
so
n
can't be maximum.
2. (a) The greatest lower bound of natural numbers is their greatest common divisor. Since the gcd of
any two elements of this poset is, in each case, still an element of the poset, every pair of elements
has a glb.
(b) The least upper bound of natural numbers is their least common multiple. The lcm of 4 and 6 is
12. Since 12 is not in the poset, 4 and 6 have no lub.
(c) This is not a lattice (because not all pairs of elements have a lub.)
3. (a) [BB]
4
6
V1
0
0
(6)
8
9
2
3
5
7
7
1
4. (a) 2, 3, 5 and 7 are minimal; 4,5, 6 and 7 are maximal. There are no minimum nor maximum
elements.
(b) 1 is minimal and minimum; 6, 7, 8, 9 and 10 are maximal. There is no maximum.
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory

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