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# Let X and Y be non-empty sets. If A_1 and A_2 are subsets of X, and B_1 and B_2 subsets of Y. Show that (A_1×B_1)U(A_2×B_2) = (A_1UA_2)×(B_1UB_2).

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Topology
Sets and Functions (XLIV)
Functions

Let X and Y be non-empty sets. If A_1 and A_2 are subsets of X and B_1and B_2 subsets of Y,
show that
(A_1×B_1)U(A_2×B_2) = (A_1UA_2)×(B_1UB_2).

See the attached file.

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#### Solution Preview

Topology
Sets and Functions (XLIV)
...

#### 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. If A_1 and A_2 are subsets of X, and B_1 and B_2 subsets of Y.
Show that
(A_1×B_1)U(A_2×B_2) = (A_1UA_2)×(B_1UB_2).

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