Adios Al Mouse

EXERCISES
0.1 Examine the following formal descriptions of sets so that you understand which
members they contain. Write a short informal English description of each set.
a. {1,3,5,7, ... }
b.{..., -4, -2,0,2,4,...}
c. {nj n = 2m for some m in AN}
d. {nj n = 2m for some m in XA, and n = 3k for some k in AV}
e. {wl w is a string of Os and is and w equals the reverse of w}
f. {nj n is aninteger and n = n + 1}
0.2 Write formal descriptions of the following sets
a. The set containing the numbers 1, 10, and 100
b. The set containing all integers that are greater than 5
c. The setcontaining all natural numbers that are less than 5
d. The set containing the string aba
e. The set containing the empty string
f. The set containing nothing at all
26 CHAPTER 0/ INTRODUCTION
0.3Let A be the set {x, y, z} and B be the set {x, y}.
a. Is A a subset of B?
b. Is B a subset of A?
c. What is A U B?
d. WhatisA nB?
e. What is A x B?
f What is the power set of B?
0.4 If A has aelements and B has b elements, how many elements are in A x B?
Explain your answer.
0.5 If C is a set with c elements, how many elements are in the power set of C? Explain
your answer.
0.6 Let X bethe set {1, 2, 3, 4, 5} and Y be the set {6, 7, 8, 9, 10}. The unary function
f: X- Y and the binary function g: X x Y- Y are described in the following
tables.
n f(n) g 6 7 8 9 10
1 6 1 10 10 1010 10
2 7 2 7 8 9 10 6
3 6 3 7 7 8 8 9
4 7 4 9 8 7 6 10
5 6 5 6 6 6 6 6
a. What is the value of f (2)?
b. What are the range and domain off?
c. What is the value of g(2, 10)?
d. What are therange and domain of g?
e. What is the value ofg(4, f(4))?
0.7 For each part, give a relation that satisfies the condition.
a. Reflexive and symmetric but not transitive
b. Reflexive and transitivebut not symmetric
c. Symmetric and transitive but not reflexive
0.8 Consider the undirected graph G= (V, E) where V, the set of nodes, is {1, 2,3, 4}
and E, the set of edges, is {{1,2}, {2,3},...