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    characteristic functions of subsets satisfy the properties

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    Prove that the characteristic functions of subsets satisfy the foowing properties:
    (a) f_(A intersection B) (x) = f_A (x) f_B (x) for all x,
    (b) f_(A union B) (x) = f_A (x) + f_B (x) - f_A (x) f_B (x) for all x,
    (c) f_(A symmetric difference B) (x) = f_A (x) + f_B (x) - 2f_A (x) f_B (x)
    for all x.

    The complete problem is in the attached file.

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    https://brainmass.com/math/discrete-structures/characteristic-functions-subsets-satisfy-properties-630661

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    The solution is in the attached file.

    Descrete Structures (I)
    By:- Thokchom Sarojkumar Sinha

    Prove that the characteristic functions of subsets satisfy the following
    properties :

    Solution:- (a) If
    then

    if and only if
    if and only if
    if and only if
    if and only if

    Therefore

    for

    Again, suppose

    if and only if
    ...

    Solution Summary

    It describes the characteristic functions of subsets satisfy the properties of
    (a) f_(A intersection B) = f_A f_B
    (b) f_(A union B) = f_A + f_B - f_A f_B
    (c) f _(A symmetric difference B) = f_A + f_B - 2f_A f_B
    The solution is given in detail.

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