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Explain the Union of Sets using set notation.
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The union of sets A and B, denoted by A ∪ B, combines all elements of both sets.
What properties are important in set operations?
Commutative, Associative, Identity, and Distributive Laws.
Define an Empty Set and its representation.
An Empty Set, also called a null set or void set, is a set with no elements. It is represented by {} or Φ.
What is a Subset and give an example?
A subset is a set where all elements are contained within another set. Example: {1, 2} is a subset of {1, 2, 3}.
What is depicted by the shaded region when using a Venn Diagram for the union of two sets?
The shaded region shows all elements that belong to either one of the sets or both.
What is a Singleton Set?
A set with only one element.
Describe the Difference of Sets A and B.
The difference of sets A and B, denoted by A - B, consists of elements in A but not in B.
Illustrate with an example a set in Roster Form and Set Builder Form.
Roster Form: {1, 3, 5} | Set Builder Form: {x | x is an odd number less than 6}
What is an example of a set in Set Builder Form?
{x | x is a vowel in the English alphabet}
Define a Superset.
A superset is a set that contains all elements of another set, and possibly more.
Convert the Roster Form {2, 4, 6} into Set Builder Form.
{x | x is an even number between 1 and 7}
When are two sets considered Equal Sets?
Two sets are equal if they contain exactly the same elements, regardless of the order of elements.
What is a set in mathematics?
A well-defined collection of objects.
Differentiate between Finite and Infinite Sets.
A Finite Set has a fixed number of elements, whereas an Infinite Set has an unlimited number of elements.
What is the Intersection of Sets?
The intersection of sets A and B, denoted by A ∩ B, consists of elements that are common to both sets.
How are Venn Diagrams used in set theory?
Venn Diagrams visually depict set operations, using rectangles for universal sets and circles for subsets to show union, intersection, and complement.
What is the Complement of a Set?
The complement of a set A, denoted by A', consists of elements not in set A but in the universal set.
Describe Roster Form in set notation.
All elements are listed, separated by commas, and enclosed in braces {}. Order does not matter, and no element is repeated.
What is a Universal Set?
A set that contains all possible elements for a particular discussion.
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