Question

For any set A and B ,the set notation of A-B is

Answer 1

The difference of set B from set A, denoted by A-B, is the set of all the elements of set A that are not in set B. In mathematical term, A-B = { x: x∈A and x∉B} If (A∩B) is the intersection between two sets A and B then, A-B = A - (A∩B)

Answer 2

Common Symbols Used in Set Theory

Symbols save time and space when writing. Here are the most common set symbols

In the examples C = {1, 2, 3, 4} and D = {3, 4, 5}

Symbol Meaning Example

{ } Set: a collection of elements {1, 2, 3, 4}

A ∪ B Union: in A or B (or both) C ∪ D = {1, 2, 3, 4, 5}

A ∩ B Intersection: in both A and B C ∩ D = {3, 4}

A ⊆ B Subset: every element of A is in B. {3, 4, 5} ⊆ D

A ⊂ B Proper Subset: every element of A is in B,

but B has more elements. {3, 5} ⊂ D

A ⊄ B Not a Subset: A is not a subset of B {1, 6} ⊄ C

A ⊇ B Superset: A has same elements as B, or more {1, 2, 3} ⊇ {1, 2, 3}

A ⊃ B Proper Superset: A has B's elements and more {1, 2, 3, 4} ⊃ {1, 2, 3}

A ⊅ B Not a Superset: A is not a superset of B {1, 2, 6} ⊅ {1, 9}

Ac Complement: elements not in A Dc = {1, 2, 6, 7}

When set universal = {1, 2, 3, 4, 5, 6, 7}

A − B Difference: in A but not in B {1, 2, 3, 4} − {3, 4} = {1, 2}

a ∈ A Element of: a is in A 3 ∈ {1, 2, 3, 4}

b ∉ A Not element of: b is not in A 6 ∉ {1, 2, 3, 4}

∅ Empty set = {} {1, 2} ∩ {3, 4} = Ø

set universal Universal Set: set of all possible values

(in the area of interest)  

     

P(A) Power Set: all subsets of A P({1, 2}) = { {}, {1}, {2}, {1, 2} }

A = B Equality: both sets have the same members {3, 4, 5} = {5, 3, 4}

A×B Cartesian Product

(set of ordered pairs from A and B) {1, 2} × {3, 4}

= {(1, 3), (1, 4), (2, 3), (2, 4)}

|A| Cardinality: the number of elements of set A |{3, 4}| = 2

     

| Such that { n | n > 0 } = {1, 2, 3,...}

: Such that { n : n > 0 } = {1, 2, 3,...}

∀ For All ∀x>1, x2>x

∃ There Exists ∃ x | x2>x

∴ Therefore a=b ∴ b=a

     

Natural Numbers Natural Numbers {1, 2, 3,...} or {0, 1, 2, 3,...}

Integers Integers {..., −3, −2, −1, 0, 1, 2, 3, ...}

Rational Numbers Rational Numbers  

Algebraic Numbers Algebraic Numbers  

Real Numbers Real Numbers  

Imaginary Numbers Imaginary Numbers 3i

Complex Numbers Complex Numbers 2 + 5i