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

D
A
means Set
"D"
IS
NOT a
Subset
of Set
"A":

Example 1:
, *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
A

Example 2:
, *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
B

Example 3:
, *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
C