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

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.

See the attached file.

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Topology

Sets and Functions (XLIII)

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#### 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.