L02 - Set Notation (aka Formal Notation)

Set Notation (Ex 8B)

Formal notation for Venn diagrams and two-way tables

• A set is a collection or group of elements that can include numbers, letters, or other objects.
• u, $\omega$, or S is called the sample space or universal set. (See the last lesson for more information about the Sample Space.)
  • set containing everything relevant to the question
  • e.g. six-sided die
    • $S=\{1,2,3,4,5,6\}$

Terminology

Example

• $S=\{1,2,3,4,5,6,7\}$
• $A=\{2,4,6\}$
• $B=\{1,2,3,5\}$

• $\in$ - belongs to a set
  • e.g. 2, 4, 6 are elements of set A
    • $2\in A$
    • $3\notin A$
• $A^{\prime }or{A}^c$ - complement of a set (not in set)
  • e.g. Complement of set A (not A) is $A^{\prime }$ or $A^c$
    • $A^{\prime }=\{1,3,5,7\}$
  • In a venn diagram, everything except A and $A\cap B$ is what is involved in $A^{\prime }$
• $n()$ - cardinal number (number of elements)
  • e.g. The cardinal number of…
    • A would be $n(A)=3$
    • B would be $n(B)=4$
• $\varnothing$ - empty/null set
  • $\varnothing =\{\}$
• A only - set of elements only in A
  • e.g. $\boxed{A\; only}=\{4,6\}$
• $\cup$ - union (“or”), all the elements that are in the selected sets
  • e.g. All the elements that are in A or B, or both.
    • $A\cup B=\{2,4,6,1,3,5\}$
    • In a venn diagram, everything in A and B will be selected.
• $\cap$ - intersection (“and”), all the elements that are in all specified sets
  • e.g. All the elements that are in A AND also in B.
    • $A\cap B=\{2\}$
    • In a venn diagram, only the intersection between A and B would be selected.
• $\subset$ - subset, all the elements of the specified set are in another set
  • e.g. A is a subset of S because all elements of A are also in S.
    • $S=\{1,2,3,4,5,6,7\}$
    • $A=\{2,4,6\}$
    • $B=\{1,2,3,5\}$
      • $A\subset S$
      • $A\not\subset B$