Math Sets G10

Comprehension

(also known as set builder notation) : expressed in the form of B={x/x is_____________ } ex : A={ x∈ IN /x is a prime number <14} hence A={1,3,5,7,11,13} (in extension)

Set

• is a group of objects (elements) • it is denoted by A={x,y,z...}

disjoint sets

A∩B =∅ ( no common elements between both sets) -card(A∩B) = card ∅ = 0

Parts of a set P(A)

all subsets of a set ex: A={1,3} then, P(A)={∅;{1};{3};{1,3}}

∈

belongs (elements wrt sets)

Card A∪B

card A + card B - card A∩B

card of P(A)

card P(A)= 2ᶜᵃʳᵈ ⁽ᴬ⁾

∉

does not belong (elements wrt to sets)

⊄

doesnt subset (set wrt set)

complement of a set

everything but a specific set [ᴬₑ , (ᴬₑ , Ā __ note: Ā= A

finite set

has a cardinal

infinite set

has no card ∞

singleton set

has only one element : D={5}

pair set

has only two elements : G={x,y}

∅

is subset of all sets

Cardinal of a set

is the number of elements in a set note that: -card 0 = nonsense -card ∅ = 0

ℚ

set of all rational numbers ex: a/b where a in Z and b in Z*

𝔻

set of decimals ex: -4,-2.3, 1,4, 5.6.....

ℤ

set of integers ex: -1,-2,-3,0,1,2,4

ℕ

set of natural numbers ex: 1,2,4,5,7,8,0...

ℝ

set of real numbers ex: sets N,D,Z,Q + radicals

Equal sets

sets with the same elements & the same card

⊂

subset (set wrt set)

ℕ* (or any other set*)

the entire set excluding 0

Representation of a set

ven diagram

Extension

• (also known as roster notation) : expressed by numbers, letters, words, symbols.... ex : X= {1,2,3,5,6,7} Y= {a,e,h,g,j,w} Z={math,physics,chemistry,biology,geography}

Intersection of sets ∩

•set of common elements btw 2 or more sets • if x ∈ A∩B then x∈A【&】x∈B

Union of sets ∪

•the combination of all elements from two or more sets ( not necessarily having common elements, however if present no repetition) •if x ∈ A∪B then x∈A 【ｏｒ】x∈B

Empty set (void)

∅ or F={}