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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
Document
... One-to-one correspondence Two sets M and N are equivalent … if it is possible to put them, by some law, in such a relation to one another that to every element of each one of them corresponds one and only one element of the other. If M and N are equivalent we often say that they have they have the ...
... One-to-one correspondence Two sets M and N are equivalent … if it is possible to put them, by some law, in such a relation to one another that to every element of each one of them corresponds one and only one element of the other. If M and N are equivalent we often say that they have they have the ...
Chap4 - Real Numbers
... One-to-one correspondence Two sets M and N are equivalent … if it is possible to put them, by some law, in such a relation to one another that to every element of each one of them corresponds one and only one element of the other. If M and N are equivalent we often say that they have they have the ...
... One-to-one correspondence Two sets M and N are equivalent … if it is possible to put them, by some law, in such a relation to one another that to every element of each one of them corresponds one and only one element of the other. If M and N are equivalent we often say that they have they have the ...
Bijective Correspondences and Countably Infinite Sets
... Two sets have the same cardinality if �and only if) it is possible to match each element of A to an element of B in such a way that every element of each set has exactly one “partner” in the other set. This might not be particularly important/interesting in the case of finite sets, since we can often ...
... Two sets have the same cardinality if �and only if) it is possible to match each element of A to an element of B in such a way that every element of each set has exactly one “partner” in the other set. This might not be particularly important/interesting in the case of finite sets, since we can often ...
Section 1.1 - GEOCITIES.ws
... You shall be able to write a given interval in set-builder notation. [Problems 83 – 90] ...
... You shall be able to write a given interval in set-builder notation. [Problems 83 – 90] ...