Sets and Subsets

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What is a set in mathematics?

Back

A set is a collection of distinct objects, considered as an object in its own right. Sets are usually denoted by curly braces, e.g., A = {1, 2, 3}.

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What is a subset?

Back

A subset is a set where all elements of the subset are also elements of another set. If A is a subset of B, it is denoted as A ⊆ B.

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What does it mean for two sets to be equal?

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Two sets A and B are equal if they contain exactly the same elements, denoted as A = B.

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What is the intersection of two sets?

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

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What is the complement of a set?

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The complement of a set A, denoted as A', is the set of all elements not in A, relative to a universal set.

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How do you determine the number of elements in a set?

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The number of elements in a set is denoted as n(A) and is simply the count of distinct elements in the set A.

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What is a Venn diagram?

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A Venn diagram is a visual representation of sets and their relationships, showing how sets intersect, union, and differ.

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What does it mean for one set to be a proper subset of another?

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A set A is a proper subset of set B if all elements of A are in B, and B contains at least one element not in A, denoted as A ⊂ B.

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What is the difference between a finite set and an infinite set?

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A finite set has a limited number of elements, while an infinite set has an unlimited number of elements.