Intro to Set Theory

Front

What is a set?

Back

A set is a collection of distinct objects, considered as an object in its own right. For example, the set of natural numbers is {1, 2, 3, ...}.

Front

What is an element of a set?

Back

An element is an individual object within a set. For example, in the set {2, 3, 5}, the number 3 is an element.

Front

What is the symbol for 'is an element of'?

Back

Front

What is the roster notation?

Back

Roster notation lists all the elements of a set explicitly. For example, the set of vowels can be written as {a, e, i, o, u}.

Front

What is set builder notation?

Back

Set builder notation describes a set by stating the properties that its members must satisfy. For example, {x | x < 5} describes the set of all x that are less than 5.

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What is the universal set?

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The universal set is the set that contains all possible elements for a particular discussion or problem. It is usually denoted by the symbol U.

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What is the empty set?

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The empty set, denoted by {}, is a set that contains no elements.

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What is a subset?

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A subset is a set where all its elements are also contained in another set. For example, {1, 2} is a subset of {1, 2, 3}.

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What is the intersection of two sets?

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The intersection of two sets A and B, denoted by A ∩ B, is the set of elements that are common to both A and B.

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What is the union of two sets?

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The union of two sets A and B, denoted by A ∪ B, is the set of elements that are in A, in B, or in both.