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SETS

Objectives: By the end of class, I will be able to: Identify sets Understand subsets, intersections, unions, empty sets, finite and infinite sets, universal sets and complements of a set. SETS. SETS. Set – a well defined collection of elements

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SETS

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  1. Objectives: By the end of class, I will be able to: • Identify sets • Understand subsets, intersections, unions, empty sets, finite and infinite sets, universal sets and complements of a set SETS

  2. SETS • Set – a well defined collection of elements • A set is often represented by a capital letter. • The set can be described in words or its members or elements can be listed with braces { } . Example: if A is the set of odd counting numbers less than 10 then we can write: • A = the set of all odd counting numbers less than ten OR • A = {1,3,5,7,9 } • To show that 3 is an element of A, we write: 3 ϵ A • To show 2 is not an element of A, we write : 2  A

  3. SETS • If the elements of a set form a pattern, we can use 3 dots. • Example: {1,2,3… } names the set of counting numbers • Another way to describe a set is by using set-builder notation. • Example: {n|n is a counting number} • This is read – the setof all elements nsuch thatn is a counting number.

  4. SETS • Finite set – a set whose elements can be counted, and in which the counting process comes to an end. • Examples: • The set of students in a class • {2,4,6,8…..200} • {x | x is a whole number less than 20} • Infinite set – a set whose elements cannot be counted • Examples: • The set of counting numbers • { 2,4,6,8… } • Empty set or null set, is the set that has no elements • Examples: • The set of months that have names beginning with the letter Q • { x | x is an odd number exactly divisible by 2 } • Symbol for the empty set { } or Ø • Universal set - is the entire set of elements under consideration in a given situation and is usually denoted by the letter U. • Example: • Scores on a Math test. U = {0,1,2 …100 }

  5. SETS • Subsets – set A is a subset of B if every element of set A is an element of set B. • We write: A  B • Example: • the set A = {Harry, Paul } is a subset of the set B = {Harry, Sue, Paul, Mary } • The set of odd whole numbers {1,3,5,7… } is a subset of the set of whole numbers, {0,1,2,3… }

  6. SETS • Union – is the set of all elements that belong to set A or to set B, or to both set A and set B. • Symbol: A υ B • Example: • If A = {1,2,3,4 } and B = { 2,4,6 }, then A υ B = {1,2,3,4,6} • Intersection - is the set of all elements that belong to both sets A and B. • Symbol: A ∩ B • Example: • If A = {1,2,3,4,5} and B = {2,4,6,8,10} then A ∩ B = { 2,4 }

  7. SETS • Complement – is the set of all elements that belong to the universe U but do not belong to the set A. • Symbol: A or Ac or A` all read A prime • Example: • If A = {3,4,5} and U = {1,2,3,4,5} , then Ac = { 1,2 } • Practice with sets

  8. Set notation Let’s review and look at Notes from regentsprep

  9. Set notation Let’s practice

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