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