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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