Homework #3
... If there is a person p who knows everyone in the group, then there cannot also be a person r who knows nobody else. Either p and r know each other (and thus r knows someone), or they do not (and thus p does not know everyone). Thus R can contain either 0 or n – 1, but not both, so in no case can R h ...
... If there is a person p who knows everyone in the group, then there cannot also be a person r who knows nobody else. Either p and r know each other (and thus r knows someone), or they do not (and thus p does not know everyone). Thus R can contain either 0 or n – 1, but not both, so in no case can R h ...
CSE 1400 Applied Discrete Mathematics Fall 2016 Practice Quiz 4
... 2. (10 pts) Let a and m be integers. Write a ⊥ m if 1 is the only integer that divides both a and m. Another way to say this is: The greatest common divisor gcd(a, m) is 1. If a ⊥ m, say a and m are said to be relatively prime (some call it co-prime). (a) Which is True and which is False: 12 ⊥ 3? 12 ...
... 2. (10 pts) Let a and m be integers. Write a ⊥ m if 1 is the only integer that divides both a and m. Another way to say this is: The greatest common divisor gcd(a, m) is 1. If a ⊥ m, say a and m are said to be relatively prime (some call it co-prime). (a) Which is True and which is False: 12 ⊥ 3? 12 ...
Exercises 3 Function Domain, codomain, range, graph
... D = set of all the modules of the HTW Tourism bachelor programme B = set of all the HTW lecturers f: D B, m ↦ l = f(m) = lecturer of m ...
... D = set of all the modules of the HTW Tourism bachelor programme B = set of all the HTW lecturers f: D B, m ↦ l = f(m) = lecturer of m ...
CHAP02 Axioms of Set Theory
... we start with in order to do this? At least most religious creeds can claim to be consistent, which is more than seems to be the case with the ZF axioms. These have never been proved consistent – but then they have never been proved inconsistent. We haven’t even got a proof that it is a logical impo ...
... we start with in order to do this? At least most religious creeds can claim to be consistent, which is more than seems to be the case with the ZF axioms. These have never been proved consistent – but then they have never been proved inconsistent. We haven’t even got a proof that it is a logical impo ...
dt248 dm review fall 2015
... 15) Draw the directed graph of the relation T on X = {1,2,3,4} defined by T = {(1,1), (2,2), (2,3),(3,2),(4,2),(4,4)}. 16) Let A = {1,2,3,4}, B = {a,b,c,d}, and C = {x,y,z}. Consider the relations R from A to B and S from B to C defined by R = {(1,a),(2,d),(3,a),(3,b),(3,d)}, S = {(b,x), (b,z), (c,y ...
... 15) Draw the directed graph of the relation T on X = {1,2,3,4} defined by T = {(1,1), (2,2), (2,3),(3,2),(4,2),(4,4)}. 16) Let A = {1,2,3,4}, B = {a,b,c,d}, and C = {x,y,z}. Consider the relations R from A to B and S from B to C defined by R = {(1,a),(2,d),(3,a),(3,b),(3,d)}, S = {(b,x), (b,z), (c,y ...
Math 232 Projects
... a. What is a partial order on X . What is a total order on X . b. Give examples of partial and total orders. c. What is a partially ordered set. Give an example of a partially ordered set. d. Does every partially ordered set have a smallest element. e. State the definition of a well-ordered set for ...
... a. What is a partial order on X . What is a total order on X . b. Give examples of partial and total orders. c. What is a partially ordered set. Give an example of a partially ordered set. d. Does every partially ordered set have a smallest element. e. State the definition of a well-ordered set for ...
CHAP03 Sets, Functions and Relations
... If R and S are relations on the set X then the sum of R and S is the relation R + S defined on X by: x(R+S)y if xRy or xSy. As sets, this is simply the union: S + T = S ∪ T. Example 10: The relation “spouse of” means “husband or wife of”. If H = “husband of” and W = “wife of” then H + W is the relat ...
... If R and S are relations on the set X then the sum of R and S is the relation R + S defined on X by: x(R+S)y if xRy or xSy. As sets, this is simply the union: S + T = S ∪ T. Example 10: The relation “spouse of” means “husband or wife of”. If H = “husband of” and W = “wife of” then H + W is the relat ...
The Number of Topologies on a Finite Set
... In this paper, we compute T (n, k) for 2 ≤ k ≤ 12, as well as the total number of labeled T0 topologies on X having n + 4, n + 5, n + 6 open sets. We also give different proofs (shorter or simpler) of some known results in [1, 3, 2]. We need some preliminary definitions and results. Let us recall th ...
... In this paper, we compute T (n, k) for 2 ≤ k ≤ 12, as well as the total number of labeled T0 topologies on X having n + 4, n + 5, n + 6 open sets. We also give different proofs (shorter or simpler) of some known results in [1, 3, 2]. We need some preliminary definitions and results. Let us recall th ...
Ribet — Final - Math Berkeley
... 7 (10 points). Let G be the simple graph whose vertices are the bit strings of length 6, two bit strings being connected by an edge if and only if they differ in exactly one place. (a) Does G have an Euler circuit? (b) Is the graph G planar? It seems to me that there are 6 edges coming out of every ...
... 7 (10 points). Let G be the simple graph whose vertices are the bit strings of length 6, two bit strings being connected by an edge if and only if they differ in exactly one place. (a) Does G have an Euler circuit? (b) Is the graph G planar? It seems to me that there are 6 edges coming out of every ...
