Union, Intersection, and Dierence of Sets · Intersection If A and B are sets, the intersection C...

Union, Intersection, and Di�erence of Sets

Union, Intersection, and Di�erence of Sets

UnionIf A and B are sets, the union C of A and B, written C = A fi B, isthe set of elements of either A or B or both.

A fi B = {x : x œ A or x œ B}.

{1, 2, 3} fi {3, 5, 6} = {1, 2, 3, 5, 6}

inunion is

inclusive or

O

A BAVB

IntersectionIf A and B are sets, the intersection C of A and B, writtenC = A fl B, is the set of elements in both A and B.

A fl B = {x : x œ A and x œ B}.

{1, 2, 3} fl {3, 5, 6} = {3}I

3

Di�erenceIf A and B are sets, the di�erence C of A and B, writtenC = A ≠ B, is the set of elements in A but not in B.

A ≠ B = {x : x œ A and x ”œ B}.

{1, 2, 3} ≠ {3, 5, 6} = {1, 2} A B

B A x x c B but X A

5,6

ExampleA = {0, 1} and B = {1, 2}. What is (A ◊ B) fl (B ◊ B)?

AXB n BXB

Bi ail i t

t0

BxB i I Y

xBh BxB 42 Cisl

ExampleLet X = [1, 3] ◊ [1, 3] and Y = [2, 4] ◊ [2, 4] in R2. Sketch the sets

I X fi YI X fl YI X ≠ YI Y ≠ X

Ei

i

X Y

immuno

Xu Y x Y v Knx u x