Problem 71E

Let S be a subset of a universal set U. The characteristic function fs of S is the function from U to the set {0. 1) such that fs(x) = 1 if x belongs to S and fs(x) = 0 if x does not belong to S. Let A and B be sets. Show that for all x ∈ U,

Solution:

Step 1:

The given condition for S be a subset of universal set U.A new function is called the characteristic function fs of S is the function from U to the set {0. 1) such that fs(x) = 1 if x belongs to S and fs(x) = 0 if x does not belong to S. Let A and B be sets.