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- https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/Discrete_Structures/05%3A_Set_Theory/5.01%3A_Sets_and_Operations_on_SetsWe have used logical operators (conjunction, disjunction, negation) to form new statements from existing statements. In a similar manner, there are several ways to create new sets from sets that have ...We have used logical operators (conjunction, disjunction, negation) to form new statements from existing statements. In a similar manner, there are several ways to create new sets from sets that have already been defined. In fact, we will form these new sets using the logical operators of conjunction (and), disjunction (or), and negation (not).
- https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book%3A_Mathematical_Reasoning__Writing_and_Proof_(Sundstrom)/05%3A_Set_Theory/5.01%3A_Sets_and_Operations_on_SetsWe have used logical operators (conjunction, disjunction, negation) to form new statements from existing statements. In a similar manner, there are several ways to create new sets from sets that have ...We have used logical operators (conjunction, disjunction, negation) to form new statements from existing statements. In a similar manner, there are several ways to create new sets from sets that have already been defined. In fact, we will form these new sets using the logical operators of conjunction (and), disjunction (or), and negation (not).
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/04%3A_Relations/4.05%3A_Combinatorics-_Inclusion_ExclusionThis page explains the inclusion-exclusion principle for counting distinct elements in overlapping sets, detailing how to adjust for over-counting overlaps. An example with students in math courses il...This page explains the inclusion-exclusion principle for counting distinct elements in overlapping sets, detailing how to adjust for over-counting overlaps. An example with students in math courses illustrates this principle. It also defines a derangement as a permutation where no element retains its original position, and concludes with practice checkpoints on related counting problems.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_(Levin)/0%3A_Introduction_and_Preliminaries/0.3%3A_SetsThe most fundamental objects we will use in our studies (and really in all of math) are sets. Much of what follows might be review, but it is very important that you are fluent in the language of set ...The most fundamental objects we will use in our studies (and really in all of math) are sets. Much of what follows might be review, but it is very important that you are fluent in the language of set theory. Most of the notation we use below is standard, although some might be a little different than what you have seen before. For us, a set will simply be an unordered collection of objects.
- https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/Discrete_Structures/02%3A_Logical_Reasoning/2.03%3A_Open_Sentences_and_SetsIf Ais a set and y is one of the objects in the set A, we write y∈A and read this as “y is an element of A” or “y is a member of A.” For example, if B is the se...If Ais a set and y is one of the objects in the set A, we write y∈A and read this as “y is an element of A” or “y is a member of A.” For example, if B is the set of all integers greater than 4, then we could write 5∈B and 10∈B.
- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_220_Discrete_Math/4%3A_SetsThumbnail: Overlapping sets. (CC BY-SA 3.0 Unported; Chris-martin via Wikipedia).
- https://math.libretexts.org/Courses/Mt._San_Jacinto_College/Ideas_of_Mathematics/03%3A_Set_Theory_and_Logic/3.01%3A_The_BasicsThe concept of sets is a fundamental idea in mathematics. Even at the earliest stage of mathematical reasoning, the idea of sets is being used. As such a fundamental concept, this subject can be stud...The concept of sets is a fundamental idea in mathematics. Even at the earliest stage of mathematical reasoning, the idea of sets is being used. As such a fundamental concept, this subject can be studied on its own as a graduate-level course! Of course, we will not go into such detail as one would expect in such a graduate-level course. Here we will explore some basic definitions and relationships about sets so that we can ultimately apply them to some practical situations.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/A_Spiral_Workbook_for_Discrete_Mathematics_(Kwong)/04%3A_SetsThumbnail: Overlapping sets. (CC BY-SA 3.0 Unported; Chris-martin via Wikipedia).
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Math_For_Liberal_Art_Students_2e_(Diaz)/03%3A_Sets/3.01%3A_BasicsAn art collector might own a collection of paintings, while a music lover might keep a collection of CDs. Any collection of items can form a set. A set simply specifies the contents; order is not impo...An art collector might own a collection of paintings, while a music lover might keep a collection of CDs. Any collection of items can form a set. A set simply specifies the contents; order is not important. The set represented by {1, 2, 3} is equivalent to the set {3, 1, 2}. Sometimes a collection might not contain all the elements of a set. For example, Chris owns three Madonna albums. While Chris’s collection is a set, we can also say it is a subset of the larger set of all Madonna albums.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/01%3A_Basics/1.02%3A_SetsThis page offers an overview of sets as key mathematical data structures, detailing their definitions, characteristics, and notations. It emphasizes well-defined sets, membership, and element order ab...This page offers an overview of sets as key mathematical data structures, detailing their definitions, characteristics, and notations. It emphasizes well-defined sets, membership, and element order absence. Through checkpoints, it encourages analysis of set membership and subsets and introduces the empty set concept. Activities are included to explore subset relationships and object membership within sets.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/04%3A_Relations/4.02%3A_Mathematical_RelationsThis page discusses the concept of relations in data organization, defining them as subsets of a Cartesian product. It covers various types of relations—reflexive, symmetric, anti-symmetric, and trans...This page discusses the concept of relations in data organization, defining them as subsets of a Cartesian product. It covers various types of relations—reflexive, symmetric, anti-symmetric, and transitive—illustrated with examples involving integers and real numbers. The text highlights specific properties and contexts, such as subset inclusion, divisibility, and the less than or equal to relation.
