Sets, set operations, and functions and relations from an intro discrete mathematics course.
35 cards · basic cards · AI-written, checked twice. Edit anything.
- What is a set?
- A collection of distinct objects (elements), unordered.
- What is an element of a set?
- An object that belongs to the set. Notation 'x in A' means x is an element of set A.
- Define roster notation.
- Writing a set by listing all its elements in braces. Example: {1, 2, 3}.
- Define set-builder notation.
- Describing a set by specifying a condition its elements satisfy. Example: {x | x is an integer and x > 0}.
- What is a subset?
- Set A is a subset of set B if every element of A is also an element of B.
- What is a proper subset?
- Set A is a proper subset of B if A is a subset of B and A is not equal to B.
- Define the union of two sets.
- A union B is the set containing all elements in A or in B (or in both).
- Define the intersection of two sets.
- A intersect B is the set containing all elements that are in both A and B.
- Define the complement of a set.
- The complement of A contains all elements in the universal set that are not in A.
- Define the difference of two sets.
- A minus B is the set of all elements in A but not in B.
- State De Morgan's First Law.
- complement(A union B) = complement(A) intersect complement(B).
- State De Morgan's Second Law.
- complement(A intersect B) = complement(A) union complement(B).
- State the distributive law for union over intersection.
- A union (B intersect C) = (A union B) intersect (A union C).
- Is the union operation commutative?
- Yes. A union B = B union A for any sets A and B.
- What is the cardinality of a set?
- The cardinality |A| is the number of distinct elements in set A.