Download Sets

Revision for Sets: See Chapter 2.1, 2.2, 2.3 and 2.4
Sets (Pages 70 -78)
Set: A collection of objects, ideas or numbers that can be clearly defined.
Elements: ∈ The objects, ideas or numbers that are members of the set.
∉ Denotes that the object etc. is not an element within the set
Braces: { } - Used to enclose the elements of a set e.g. {a,e,i,o,u}.
Roster form of a set is written e.g. A = {a,e,i,o,u}
Elipses: … indicates elements of a set not written:
e.g. {1,2,3 …10} finite set
{1,2,3 …}
infinite set
Set builder notation: describes what the set is in a simpler form, using a vertical line (|) to stand for ‘such
that’. e.g. A = {𝓍 | 𝓍 is an even counting number} see Page 73/74.
Empty or null set: { } or ∅ represents a set with no elements. ( NB. it is not written {∅}).
Subsets (Pages 78 – 82):
Subset: A ⊆ B Given any two sets A and B, if every element in A is also an element in B, then A is a subset of
B. This includes the subset of the set itself.
Proper subset: A ⊂ B – If A is a subset of B and there is at least one element of B that is not contained in A,
the A is a proper subset of B.
How to find the number of subsets: If a set contains n elements, then if contains 2n subsets.
How to find the number of proper subsets: If a set contains n elements, then if contains 2n -1 proper subsets.
Universal Set: Is the set that contains everything we are interested in now in a given problem and is
denoted by U.
Complement: This is everything in the universal set U but not in set A. The symbol for the complement is A’.
Set Operations (Pages 82 – 86)
Intersection: A ⋂ B If there are two dets A and B, then the intersection of A and B is the set of elements that
are members of both A and B.
Union: A ⋃ B If there are two sets A and B, then the Union of A and B is the total set of elements from both A
and B.
Know how to calculate (A ⋂ B)’ (A ⋂ B) ⋃ C
within the parenthesis (brackets) first.
A’ ⋃ B’
(A ⋃ B)’ etc. Remember to calculate operation
Set builder notation Know the definition of intersection and union of two sets in set builder notation.
**PRACTICE THE EXAMPLES AND EXERCISES FROM THE TEXT BOOK**