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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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.
Solution Preview
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
...
Education
- BSc, Manipur University
- MSc, Kanpur University
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