sets_flashcards
What is a set?
A collection of distinct objects, called elements.
How do you denote a set?
Using curly brackets, e.g., S = {1, 2, 3}.
What does x ∈ S mean?
x is an element of set S.
What does x ∉ S mean?
x is not an element of S.
What is the empty set?
A set with no elements, denoted ∅ or {}.
What is a finite set?
A set with a countable number of elements.
What is an infinite set?
A set with an uncountable number of elements.
What are common sets in mathematics?
Natural numbers (N), Integers (Z), Rational numbers (Q), Real numbers (R).
What is roster notation?
Listing elements explicitly, e.g., A = {1, 2, 3, 4}.
What is set-builder notation?
Defining a set using a condition, e.g., A = {x | x is an even number}.
What is a subset?
A set A is a subset of B (A ⊆ B) if every element of A is in B.
What is a proper subset?
A subset that is not equal to the original set (A ⊂ B).
What is the power set of a set S?
The set of all subsets of S, denoted power(S).
What is the union of two sets (A ∪ B)?
The set of all elements in A or B or both.
What is the intersection of two sets (A ∩ B)?
The set of all elements common to both A and B.
What is the difference of two sets (A - B)?
The set of elements in A but not in B.
What is the complement of a set A (A’)?
The set of all elements not in A (relative to a universal set).
What is a Venn diagram?
A visual representation of sets and their relationships.
What does A ∩ B look like in a Venn diagram?
The overlapping region between two circles representing A and B.
What does A ∪ B look like?
The entire area covered by both circles A and B.
How do you prove A ⊆ B?
Show that every element of A is in B.
How do you prove two sets are equal (A = B)?
Show A ⊆ B and B ⊆ A.
What does it mean if A ∩ B = ∅?
Sets A and B are disjoint (no common elements).
