{ }

a collection of elements

A = {3,7,9,14},
B = {9,14,28}

A ∩ B

objects that belong to set A and set B

A ∩ B = {9,14}

A ∪ B

objects that belong to set A or set B

A ∪ B = {3,7,9,14,28}

A ⊆ B

subset has fewer elements or equal to the set

{9,14,28} ⊆ {9,14,28}

A ⊂ B

subset has fewer elements than the set

{9,14} ⊂ {9,14,28}

A ⊄ B

left set not a subset of right set

{9,66} ⊄ {9,14,28}

A ⊇ B

set A has more elements or equal to the set B

{9,14,28} ⊇ {9,14,28}

A ⊃ B

set A has more elements than set B

{9,14,28} ⊃ {9,14}

A ⊅ B

set A is not a superset of set B

{9,14,28} ⊅ {9,66}

2^{power set}

all subsets of A

all subsets of A

A = B

both sets have the same members

A={3,9,14},
B={3,9,14},
A=B

A^c

all the objects that do not belong to set A

A \ B

objects that belong to A and not to B

A = {3,9,14},
B = {1,2,3},
A-B = {9,14}

A – B

objects that belong to A and not to B

A = {3,9,14},
B = {1,2,3},
A-B = {9,14}

A ∆ B

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

A = {3,9,14},
B = {1,2,3},
A ∆ B = {1,2,9,14}

A ⊖ B

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

A = {3,9,14},
B = {1,2,3},
A ⊖ B = {1,2,9,14}

a∈A

set membership

A={3,9,14}, 3 ∈ A

x∉A

no set membership

A={3,9,14}, 1 ∉ A

(a,b)

collection of 2 elements

A×B

set of all ordered pairs from A and B

|A|

the number of elements of set A

A={3,9,14}, |A|=3

#A

the number of elements of set A

A={3,9,14}, #A=3

infinite cardinality of natural numbers set

cardinality of countable ordinal numbers set

Ø

Ø = { }

C = {Ø}

set of all possible values

₀ = {0,1,2,3,4,…}

0 ∈ ₀

₁ = {1,2,3,4,5,…}

6 ∈ ₁

= {…-3,-2,-1,0,1,2,3,…}

-6 ∈

= {x | x=a/b, a,b∈}

2/6 ∈

= {x | -∞ < x <∞}

6.343434 ∈

= {z | z=a+bi, -∞<a<∞, -∞<b<∞}

6+2i ∈