# characteristic functions of subsets satisfy the properties

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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