Set theory

Symbol

Symbol Name

Meaning 

Example

{ }

set

a collection of elements

A = {1, 7, 9, 13, 15, 23},

B = {7, 13, 15, 21}

A ∪ B

union

Elements that belong to set A or set B

A ∪ B = {1, 7, 9, 13, 15, 21, 23}

A ∩ B

intersection

Elements that belong to both the sets, A and B

A ∩ B = {7, 13, 15 }

A ⊆ B

subset

subset has few or all elements equal to the set

{7, 15} ⊆ {7, 13, 15, 21}

A ⊄ B

not subset

left set is not a subset of right set

{1, 23} ⊄ B

A ⊂ B

proper subset / strict subset

subset has fewer elements than the set

{7, 13, 15} ⊂ {1, 7, 9, 13, 15, 23}

A ⊃ B

proper superset / strict superset

set A has more elements than set B

{1, 7, 9, 13, 15, 23} ⊃ {7, 13, 15, }

A ⊇ B

superset

set A has more elements or equal to the set B

{1, 7, 9, 13, 15, 23} ⊇ {7, 13, 15, 23}

Ø

empty set

Ø = { }

C = {Ø}

P (C)

power set

all subsets of C

C = {4,7},

P(C) = {{}, {4}, {7}, {4,7}}

Given by 2^s, s is number of elements in set C

A ⊅ B

not superset

set X is not a superset of set Y

{1, 2, 5} ⊅{1, 6}

A = B

equality

both sets have the same members

{7, 13,15} = {7, 13, 15}

A \ B or A-B

relative complement

objects that belong to A and not to B

{1, 9, 23}

A^c

complement

all the objects that do not belong to set A

We know, U = {1, 2, 7, 9, 13, 15, 21, 23, 28, 30}

A^c = {2, 21, 28, 30}

A ∆ B

symmetric difference

objects that belong to A or B but not to their intersection

A ∆ B = {1, 9, 21, 23}

a ∈ B

element of

set membership

B = {7, 13, 15, 21},

13 ∈ B

(a, b)

ordered pair

collection of 2 elements

(1, 2)

x ∉ A

not element of

no set membership

A = {1, 7, 8, 13, 15, 23}, 5 ∉ A

|B|

cardinality

the number of elements of set B

B = {7, 13, 15, 21}, |B|= 4

A × B

cartesian product

set of all ordered pairs from A and B

{3,5} × {7,8} = {(3,7), (3,8), (5,7), (5, 8)}

N₁

natural numbers / whole numbers  set (without zero)

N₁ = {1, 2, 3, 4, 5,…}

6 ∈ N₁

N₀

natural numbers / whole numbers  set (with zero)

N₀ = {0, 1, 2, 3, 4,…}

0 ∈ N₀

Q

rational numbers set

Q= {x | x=a/b, a, b ∈ Z}

2/6 ∈ Q

Z

integer numbers set

Z= {…-3, -2, -1, 0, 1, 2, 3,…}

-6 ∈ Z

C

complex numbers set

C= {z | z = a + bi, -∞<a<∞,                         -∞<b<∞}

6 + 2i ∈ C

R

real numbers set

R= {x | -∞ < x <∞}

6.343434 ∈ R