Examples for

Set Theory

Set theory is the mathematical theory of collections of objects. Natural questions that arise in set theory are set membership, overlap, disjointedness and equality. Use Wolfram|Alpha's symbolic capabilities to test for set membership, set equality and subset relations; to find Cartesian products of sets; and to draw Venn diagrams.
Set Theory

Perform various set-theoretic operations. Build sets with operations such as union, intersection, difference, etc.

Generate a Venn diagram:

(A union B) intersect C
symmetric difference of S and T
(complement S) intersect (A union B)

Test whether a given equation of sets is true:

is (A union B)'=(A') intersect (B')
is the set {a,b} = {a,b,a}

Determine whether one set is a subset of another:

is (X intersect Y) a subset of Y?
is complement B a subset of B union A
(X intersection (Y union Z union W)) subset (Y union X)

Compute the Cartesian product of two sets:

Cartesian product {1,2,3}, {4,5,6,7}
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