Set notation & venn diagrams

• What is a set?


  A set is a collection of elements.
• What types of elements can be included in a set?

  Elements could be anything such as numbers, letters, or coordinates.
• How would you describe a set using set notation?

  You describe a set by writing its elements inside curly brackets, e.g., {1, 2, 3, 6}.
• What does the notation {x : x < 100} represent?


  This represents the set of numbers which are less than 100 when squared.
• What does the notation {(x, y) : y = 2x + 1} represent?

  This represents the set of points that lie on the line y = 2x + 1.
• What is the universal set denoted by?

  ℰ is the universal set.
• What does the universal set ℰ represent in the context of factors of 24?

  ℰ = {1, 2, 3, 4, 6, 8, 12, 24} represents all factors of 24.
• What does the symbol ∅ represent?

  ∅ represents the empty set, which has no elements.
• Give an example of an empty set using set notation.

  {x : x is an even prime bigger than 5} = ∅.
• How do we typically denote sets and their elements?

  Upper case letters represent sets (A, B, C, ...) and lower case letters represent elements (a, b, c, ...).
• What does n(A) represent in set notation?

  n(A) represents the number of elements in set A.
• What is the value of n({1, 4, 9})?

  n({1, 4, 9}) = 3.
• What does a ∈ A mean?

  a ∈ A means a is an element of A.
• If x ∈ {1, 4, 9}, what can we conclude about x?

  x is either 1, 4, or 9.
• What does A ⊆ B signify?

  A ⊆ B means A is a subset of B, meaning every element in A is also in B.
• What does A ⊂ B indicate?

  A ⊂ B means A is a proper subset of B, meaning A is a subset of B but not the same as B.
• How is the difference between ⊆ and ⊂ similar to the difference between ≤ and <?

  The difference is that ⊆ allows for equality while ⊂ does not, similar to ≤ and <.
• Give an example of A ⊂ B.

  {1, 2, 3, 6} ⊂ {1, 2, 3, 4, 6, 8, 12, 24}.
• What does a ∉ A mean?

  a ∉ A means a is not an element of the set A.
• What does A ⊈ B signify?

  A ⊈ B means A is not a subset of B.
• What does A ⊄ B indicate?

  A ⊄ B means A is not a proper subset of B.
• What does A ∩ B represent?

  A ∩ B represents the intersection of A and B, which is the set of elements that are in both A and B.
• What does A ∪ B signify?

  A ∪ B represents the union of A and B, which is the set of elements that are in at least one of the sets.
• What does A' represent?

  A' represents "not A," which is the set of elements that are not in A.
• What is a Venn diagram?

  A Venn diagram is a way to illustrate all the elements within sets and any intersections.
• What does a rectangle in a Venn diagram represent?

  A rectangle represents the universal set (ℰ).
• What do the circles in a Venn diagram represent?

  Circles represent each set, and they may or may not overlap depending on which elements are shared between sets.
• What does A' represent in a Venn diagram?

  A' is represented by the regions that are not in the A circle.
• How is A ∩ B represented in a Venn diagram?

  A ∩ B is represented by the region where the A and B circles overlap.
• How is A ∪ B represented in a Venn diagram?

  A ∪ B is represented by the regions that are in A or B or both.
• In a Venn diagram, if two sets A and B are shown, how do you find n(A)?


  n(A) is found by counting the elements inside the A circle.
• If A = {2, 6, 12, 14, 28}, what is n(A)?

  n(A) = 5.
• If {14, 28} are elements in both A and B, how would you express this using set notation?

  {14, 28} = A ∩ B.
• If A' is the set of elements not in A, how would you find A' ∪ B?

  A' ∪ B is the set of elements that are in at least one of the sets.
• If A' = {1, 5, 7, 8, 21, 35} and B = {7, 14, 21, 28, 35}, what is A' ∪ B?


  A' ∪ B = {1, 5, 7, 8, 14, 21, 28, 35}.