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    Class of all finite unions of sets of the form A×B

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    Topology
    Sets and Functions (XLIII)
    Functions

    Let X and Y be non-empty sets and let A and B be rings of subsets of X and Y respectively.
    Show that the class of all finite unions of sets of the form A×B with A belongs to the family set A and B belongs to the family set B is a ring
    of subsets of X×Y.

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    https://brainmass.com/math/ring-theory/class-finite-unions-sets-form-147175

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    Topology
    Sets and Functions (XLIII)
    ...

    Solution Summary

    This solution is comprised of a detailed explanation of the properties of the products of sets.
    It contains step-by-step explanation of the following problem:

    Let X and Y be non-empty sets and let A and B be rings of subsets of X and Y respectively.
    Show that the class of all finite unions of sets of the form A×B with A belongs to the family set A and B belongs to the family set B is a
    ring of subsets of X×Y.

    $2.19