Math Symbols: NOT Subset (left) of Set (right)

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Math Symbols
The Most Valuable and Important
Symbols For Set Notation In Use:

"NOT Subset (left) of Set (right)"

$Math - Symbol for NOT Subset (left) of Set (right)$

Math Symbols: . . . why math symbols are used . . .

Symbols are a concise way of giving lengthy instructions related to numbers and logic.

Symbols are a communication tool. Symbols are used to eliminate the need to write long, plain language instructions to describe calculations and other processes.

For example, a single symbol stands for the entire process for addition. The familiar plus sign eliminates the need for a long written explanation of what addition means and how to accomplish it.

The same symbols are used worldwide . . .

The symbols used in mathematics are universal.

The same math symbols are used throughout the civilized world. In most cases each symbol gives the same clear, precise meaning to every reader, regardless of the language they speak.

The most valuable, most frequently used Symbols in mathematics . . .

The most important, most frequently used Symbols for Set Notation are listed below.

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$Math - Brace Symbols used to Identify Sets$

Brace Symbols
(used to
Identify Sets)

$Math - Null Set$

Null Set
(nothing included
in the
Set)

$Math - Symbol for Element of a Set$

Element of a Set
("element" of set [on left];
"complete set" [on right])

$Math - Symbol for NOT Element of a Set$

NOT Element
of a Set

$Math - Symbol for PROPER Subset (left) of Set (right)$

"Proper"
Subset (left)
of Set (right)
(the "Proper" Subset [left] is
only a part of the Set [right])

$Math - Symbol for NOT Subset (left) of Set (right)$

NOT Proper
Subset (left)
of Set (right)

$Math - Symbol for PROPER or IMPROPER Subset (left) of Set (right)$

"Proper" or "Improper"
Subset (left)
of Set (right)
("Improper Subset": the
Subset [left] and the
Set [right] are the same)

$Math - (Another) Symbol for PROPER Subset (left) of Set (right)$

"Proper"
Subset (left)
of Set (right)
(same meaning as
symbol directly above)

$Math - Symbol for Subset (right) of Set (left)$

"Proper"
Subset (right)
of Set (left)
(the Set [left] is
also called a Superset)

$Symbol for PROPER or IMPROPER Subset (right) of Set (left)$

"Proper" or "Improper"
Subset (right)
of Set (left)

$Math - (another) Symbol for PROPER Subset (right) of Set (left)$

"Proper"
Subset (right)
of Set (left)

$Math - Symbol for UNION of Two Sets$

UNION
of Two Sets

$Math - Symbol for INTERSECTION of Two Sets$

INTERSECTION
of Two Sets

$Math - Specialized Set Notations N (natural numbers), Z (integers), Q (rational numbers), and R (real numbers)$

Specialized Set Notations
(N [natural numbers],
Z [integers],
Q [rational numbers],
and R [real numbers])

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$Math - Symbol for NOT Subset (left) of Set (right)$ Math Symbol for "NOT Subset (left) of Set (right)"

D $Math - Symbol for NOT Subset (left) of Set (right)$ A means Set "D" IS NOT a Subset of Set "A":

Example 1: $Math - Symbol for NOT Subset (left) of Set (right)$ , Set A: A = { a , b , c , d}

Set D: D = { x , z }

. . . Both Set "D" and Set "A" contain completely different elements.

. . . They have nothing in common.

. . . Set D is "NOT a Subset" of Set A

D $Math - Symbol for NOT Subset (left) of Set (right)$ A

Example 2: $Math - Symbol for NOT Subset (left) of Set (right)$ , Set B: B = { 1 , 3 , 9 , 11}

Set E: E = { 9 , 55 }

. . . Both Set "E" and Set "B" do contain one common element: 9.

. . . However, in order for Set "E" to be a subset of Set "B", all of the elements in Set "E" must also be present in Set "B".

. . . The number 55 is present in Set "E", but is missing in Set "B".

. . . Set E is "NOT a Subset" of Set B

E $Math - Symbol for NOT Subset (left) of Set (right)$ B

Example 3: $Math - Symbol for NOT Subset (left) of Set (right)$ , Set C: C = {dog, cat, bird, horse, rabbit }

Set F: F = { hawk, fish }

. . . Both Set "F" and Set "C" contain completely different elements.

. . . They have nothing in common.

. . . Set F is "NOT a Subset" of Set C

F $Math - Symbol for NOT Subset (left) of Set (right)$ C