Sets, section 2.1 and 2.2

Set Concepts

• A set is a collection of objects.
• An element is an item in a set, sometimes called members.
• A set is well defined if the members of the set can be clearly determined.
• Three methods of listing a set
  • Descriptive: A is the set of all even integers between 1 and 10 inclusive.
  • Roster: A = { 2, 4, 6, 8, 10}
  • Set Builder: A = { x | x ∈ N and 1 ≤ 2x ≤ 10}
• The set N is the set of natural numbers.
• N = { 1, 2, 3, ...}
• The set A is equal to set B (A=B) if and only if A and B contain exactly the same elements.
• The cardinal number of a set A ( n(A)) is the number of elements in the set A.
• A set is finite if it contains no elements or n(A) ∈ N
• The set A is equivalent to the set B if and only if n(A) = n(B)
• The empty set {} or ∅ contains no elements.
• The universal set U, is a set that contains all elements related to a specific discussion.
• The symbol ∈ is used to show that an item is an element of a set.
• The symbol ∉ is used to show that an item is not an element of a set.
• DO examples page 50, 13, 17, 19, 21, 27, 28, 29, 33,41, 43, 46,

Subsets

• The set A is a subset of the set B if every element of A is an element of B. (A ⊆ B)
• The set A is a proper subset of the set B if, A ⊆ B and A≠ B. (A ⊂ B)
• The empty set is a subset of every set.
• If n(A) = x, then there are 2^x distinct subsets of A.
• Page 58, Do 7,9, 13, 18, 19, 28, 30, 31, 36, 38