Module 4: Sets Flashcards
Set
a well-defined collection of objects
A U B or A ____ B
Union ( combination of distinct elements )
A ∈ B or A _____ B
belongs to or is an element of
A ∉ B or A ____ B
does not belong to or is not an element of
Two types of Set Descriptions
Enumeration or Roster Method and Rule method
Enumeration or Roster Method
Elements in a set are listed down
Rule Method
Elements in a set are described
True of False: The order of the elements in a set matters.
FALSE
Equal Sets (A=B)
Two sets A and B are equal if both sets have EXACLTY THE SAME elements
Finite Set
It is possible to list down all of its elements
Infinite Set
All of its elements cannot be listed down
Cardinality of a Set
The number of elements contained in the set
Empty or Null Set (set wit no elements) is denoted by ____ or ____.
Ø or {}
Universal Set or U
the set consisting of all elements in a particular discussion
A ∩ B or A ____ B
Intersection (distinct elements found in BOTH A and B)
A \ B or A ____ B
Difference ( Distinct elements in A but not in B )
Ac or ______ of A
Complement (Distinct elements NOT in A)
A x B or _________ of A and B
Cartesian Product [ order of elements is important because the product is an ordered pair: (a,b) is not the same as (b,a) ]
The union and intersection of sets A and B belonging to a universal set U satisfy which two properties
Commutative and Associative Properties
TRUE OR FALSE: The set difference does not satisfy the commutative and associative properties.
TRUE
1st Formula for Cardinality: number of elements in A intersection B
n(A ∩ B) = n(A) + n(B) − n(A ∩ B)
2nd Formula for Cardinality: number of elements in complement of A
n(Ac) = n(U) − n(A)
3rd Formula for Cardinality: number of elements in A difference B
n(A \ B) = n(A) − n(A ∩ B)
4th Formula for Cardinality: number of elements in the cartesian product of A and B
n(A x B) = n(A) · n(B)
A ≠ B or A ____ B
not equal to
A ⊆ B or A _____ B
Subset (every distinct element of A is in B)
A ⊈ B or A _____ B
is not a subset of
A ⊂ B or A _____ B
Proper Subset (every element of A is in B, but B has more elements)
A∼B or A ____ B
is equivalent to (A and B have the SAME NUMBER of elements)
1st Property satisfied by A=B, given that A∼B
Reflexivity (if A=B, then B=A; therefore, if A∼B, then B∼A)
2nd Property satisfied by A=B, given that A∼B
Symmetry (if A=B then B=A; therefore, if A∼B, then B∼A)
3rd Property satisfied by A=B, given that A∼B
Transivity (if A=B and B=C, then A=C; therefore, if A∼B and B∼C, then A∼C)
One-to-One Correspondence
If and only if every element of A corresponds to exactly one element of B and every element of B corresponds to exactly one element of A (if there exists a bijection from set A onto B)
Aleph-null
the lowest level of infinity
TRUE OR FALSE: A set with a cardinality of aleph-null or the lowest level of infinity is infinite.
FALSE
