complex number, Algebra Formulas,Union of sets,Intersection of sets,Cartesian product,Sets of Numbers download in pdf
20 Jan 2017
experhap.blogspot.com
Algebra Formulas
1. Set identities
Definitions:
I: Universal set
A’: Complement
Empty set: ∅
Union of sets
A ∪ B = {x | x ∈ A or x ∈ B}
Intersection of sets
Identity
A ∪ ∅ =
A A ∩ I = A
Set identities involving union, intersection and complement
complement of intersection and union
A ∪ A′ = I A ∩ A′ = ∅
De Morgan’s laws
A ∩ B = {x | x ∈ A and
Complement
A′ = {x ∈ I | x ∈ A}
Difference of sets
x ∈ B}
( A ∪ B )′ = A′ ∩ B′
( A ∩ B )′ = A′ ∪ B′
Set identities involving difference
B \ A = B ( A ∪ B )
B \ A = {x | x ∈ B
Cartesian product
and
x ∉ A}
B \ A = B ∩ A′
A \ A = ∅
( A \ B ) ∩ C = ( A ∩ C ) \ ( B ∩ C )
A × B = {( x, y )| x ∈ A and
y ∈ B}
Set identities involving union
Commutativity
A ∪ B = B ∪ A
Associativity
A ∪ ( B ∪ C ) = ( A ∪ B ) ∪ C
Idempotency
A ∪ A = A
Set identities involving intersection
commutativity
A ∩ B = B ∩ A
Associativity
A ∩ ( B ∩ C ) = ( A ∩ B ) ∩ C
Idempotency
A ∩ A = A
Set identities involving union and intersection
Distributivity
A ∪ ( B ∩ C ) = ( A ∪ B ) ∩ ( A ∪ C )
A ∩ ( B ∪ C ) = ( A ∩ B ) ∪ ( A ∩ C )
Domination
A′ = I \ A
2. Sets of Numbers
Definitions:
N: Natural numbers
No: Whole numbers
Z: Integers
Z+: Positive integers
Z-: Negative integers
Q:
Rational numbers C: Complex numbers
Natural numbers (counting numbers )
N = {1, 2, 3,... }
Whole numbers ( counting numbers + zero )
No = {0, 1, 2, 3, ... }
Integers
Z + = N = {1, 2, 3,... }
Z − = {..., − 3, − 2, − 1 }
A ∩ ∅ =
∅
A ∪ I = I
Z = Z − ∪{0} ∪ Z = .{ .., − 3, − 2,
−1, 0, 1, 2, 3,... }
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