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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) intersection (A_2×B_2) = (A_1 intersection A_2)×(B_1 intersection B_2).

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    Topology
    Sets and Functions (XLI)
    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_1×B_1) intersection (A_2×B_2) = (A_1 intersection A_2)×(B_1 intersection B_2).

    See the attached file.

    © BrainMass Inc. brainmass.com October 9, 2019, 8:14 pm ad1c9bdddf
    https://brainmass.com/math/geometry-and-topology/144111

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    Topology
    Sets and Functions (XLI)
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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. 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) intersection (A_2×B_2) = (A_1 intersection A_2)×(B_1 intersection B_2).

    $2.19