# Difference of the product of sets

Topology

Sets and Functions (XLII)

Functions

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_1Ã—B_1) - (A_2Ã—B_2) = (A_1 - A_2)Ã—(B_1 - B_2)

U(A_1 intersection A_2)Ã—(B_1 - B_2)

U(A_1 - A_2)Ã—(B_1 intersection B_2)

See the attached file.

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#### Solution Preview

Topology

Sets and Functions (XLII)

Functions

Let X and Y ...

#### 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_1Ã—B_1) - (A_2Ã—B_2) = (A_1 - A_2)Ã—(B_1 - B_2)

U(A_1 intersection A_2)Ã—(B_1 - B_2)

U(A_1 - A_2)Ã—(B_1 intersection B_2)