Sets and Their Operations

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Questions and Answers

What is a set?

  • A collection that contains at least one element
  • A random collection of items
  • A collection of definite and distinct objects (correct)
  • A collection that can be infinitely large

What is an empty set?

The set that contains no elements.

What are subsets?

When every element of A is also an element of B.

What are equal sets?

<p>Sets that contain exactly the same members.</p> Signup and view all the answers

What is a universal set?

<p>The set of all possible elements from which subsets are formed.</p> Signup and view all the answers

What is the complement of a set?

<p>The set of all elements in the universal set that are not in a given set.</p> Signup and view all the answers

What is the union of sets?

<p>The set of elements in either A or B (or in both).</p> Signup and view all the answers

What is the intersection of sets?

<p>The set of elements that are in both A and B.</p> Signup and view all the answers

What is a Venn diagram?

<p>A diagram that uses circles to show comparison.</p> Signup and view all the answers

What is a proper set?

<p>Every element in a set is also an element in another set, and the sets are not equal.</p> Signup and view all the answers

What is a singleton set?

<p>A set with only one element.</p> Signup and view all the answers

What is a power set?

<p>Set of all subsets.</p> Signup and view all the answers

What is the symmetric difference of two sets?

<p>(A-B) U (B-A)</p> Signup and view all the answers

What is the cardinal number of a set?

<p>The number of distinct elements in a finite set.</p> Signup and view all the answers

What are equivalent sets?

<p>Two or more sets that have the same number of elements.</p> Signup and view all the answers

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Study Notes

Sets

  • Developed by German mathematician George Cantor (1845-1918).
  • Fundamental in relations, functions, logic, and probability theory.
  • Defined as a collection of distinct objects or elements.

Empty Set / Null Set

  • Defined as a set containing no elements.
  • Notated with open brackets: {}.

Subsets

  • A set A is a subset of B if every element of A is also an element of B.

Equal Sets

  • Two sets are equal if they contain exactly the same members.

Universal Set

  • The universal set includes all possible elements from which subsets are derived.

Complement of a Set

  • Refers to elements in the universal set that are not included in a specified set.

Union of Sets

  • Union of sets A and B is denoted as A U B.
  • Includes all elements present in either set A or set B (or both).

Intersection of Sets

  • Intersection of sets A and B is denoted as A ∩ B.
  • Contains all elements present in both sets A and B.

Venn Diagram

  • A visual representation using circles to illustrate the relationships and comparisons between different sets.

Proper Set

  • A set is a proper set if all its elements belong to another set, and they are not identical.

Singleton Set

  • A set that consists of only one element.

Power Set

  • The power set is the collection of all possible subsets of a given set.

Symmetric Difference of Two Sets

  • Denoted as A∆B which represents (A - B) U (B - A).
  • It includes elements that are in either set A or set B but not in both.

Cardinal Number of Sets

  • Refers to the number of distinct elements in a finite set, denoted as n(A).
  • Example: For A = {1, 2, 3, 4, 5}, n(A) = 5.

Equivalent Sets

  • Two or more sets are equivalent if they contain the same number of elements.

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