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.

© SolutionLibrary Inc. solutionlibary.com November 30, 2020, 12:25 am 9836dcf9d7 https://solutionlibrary.com/math/discrete-math/characteristic-functions-of-subsets-satisfy-the-properties-j7s5