Pointwise Operations and Characteristic Functions
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Let U be a set, suppose f, g : U --> R are functions from U to the set of real numbers R, and Let a E R.
Then f + g, fg. af: U --> R are defined by
(f + g)(x) = f(x) + g(x),
(fg)(x) = f(x)g(x)
(af)(x) = a(f(x))
for all x E R.
If a E R by abuse of notation we regard a as the constant function from U to R defined by a(x) = a for all x E U.
Now regard U as a universal set. For a subset A of U the characteristic fundion of A is the function A : U ?> R defined by
....
1. Let U be a universal set.
a) Let AB C U. Show that XA =XB if and only if A=B.
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Pointwise Operations and Characteristic Functions are investigated. The solution is detailed and well presented.
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