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    Proving the Main Property of a Second Set Mapping

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    Consider an arbitrary mapping f : X → Y. Suppose that f is a one-to-one onto.

    Prove the main property of the second set mapping:

    B1 is a subset of B2 implies f^(-1)(B1) is a subset of f^(-1)(B2).

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    Solution Summary

    This problem is mainly proving the main property of a second set mapping.
    The solution is given in detail.