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Sets, Note: A subset can be a proper set but a proper set cannot be a…
Sets
Types of sets
∅ or { } Empty/Null set
Set with no elements
Finite set
Set with countable elements
Infinite set
Set with endless elements
= Equal set
Two sets with the exact same elements
A={1,2,3} B={1,2,3}
≈ Equivalent set
Two sets with the
same number of elements
but not the same elements
A={1,2,3} B={a,b,c}
;Both have the same number of elements
⊂ Subset
set A
where every element
is also found in
set B
A={2,3} B={1,2,3}
or
A={a,b,c,d} B={a,b,c,d}
;A is a subset of B
Keyword: Less than or equal to
set A can be equal or less than set B
to be a subset
⊂ Proper subset
set A
where set A elements
can be found in
set B
A={1,2,3} B={1,2,3,4}
;A is a proper subset of B
Keyword: Strictly less than
Set A cannot be equal to set B
⊃ Super set
Set A
where
set B
contains all element of set A
A={1,2,3,4,5} B={1,2 }
;A is a super set of B
P(A) Power set
The set of all possible subsets of that set
B={1,2}
P(B)={∅,{1},{2},{1,2,}}
How to define a set
Roster/Tabular form
Listing all of the set elements
Set builder form
Writing condition(s) for a member to be in the set
What is a set
A well defined collection of objects
Each thing in a set is called a member or an element
Note
: A subset can be a proper set
but
a proper set cannot be a subset