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# 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.

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.

#### Solution Preview

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.

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