Math Symbols The Most Valuable and Important Symbols For Set Notation In Use:
"PROPER Subset (right) of Set (left)"
Background  why math symbols are used. . .
Symbols are a concise way of giving lengthy instructions related to
numbers and logic.
Symbols are an invention, not a discovery. They are a
communication tool. Symbols are used to eliminate
the need to write long, plain language instructions to describe
calculations and other processes.
The most valuable, most frequently used Math Symbols . . .
The most important, most frequently used Symbols for Set Notation
are listed below.
Symbols for Set Notation  click symbol
Symbol for "PROPER (1) Subset (right) of Set (left)" 
A D means Set "D" is a PROPER Subset of Set "A":
(1)
Every element (without exception) contained in Set "D" is also present in Set "A".
And . . .
(2)
Set "D" cannot be equal to Set "A". (Set "D" must have a smaller number of elements than Set "A")
Example 1:
, Set A: A = {a, b, c, d}
Set D: D = {a, c}
(1) . . .
Both Set "D" and Set "A" contain the following elements: a, c
(2) . . .
Set "D" and Set "A" are not equal. Set "A" contains more elements than Set "D".
Set D is a "Proper Subset" of Set A
A D
Example 2:
, Set B: B = {1, 3, 9, 11}
Set E: E = {9, 11}
(1) . . .
Both Set "E" and Set "B" contain the following elements: 9, 11
(2) . . .
Set "E" and Set "B" are not equal. Set "B" contains more elements than Set "E".
Set E is a "Proper Subset" of Set B
B E
Example 3:
, Set C: C = {cat, bird, dog,
horse, rabbit}
Set F: F = {rabbit, cat}
(1) . . .
Both Set "F" and Set "C" contain the following elements: cat, rabbit
(2) . . .
Set "F" and Set "C" are not equal. Set "C" contains more elements than Set "F".
Set F is a "Proper Subset" of Set C
C F
Note: the elements within a SET/SUBSET can be listed in any order.
