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    Main property of the first set mapping

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    Consider an arbitrary mapping f : X --> Y.
    Prove the main property of the first set mapping:
    A_1 is a subset of A_2 implies that f(A_1) is a subset of f(A_2).

    The attached file contains the symbol version of the above statement for clarity.

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    Solution Summary

    This posting gives all the steps in the calculations necessary as well as concluding remarks at the end.