Show that if S is a set, then there does not exist an onto

Chapter 2, Problem 40E

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QUESTION:

Show that if S is a set, then there does not exist an onto function f from S to the power set of 5. Conclude that |S|< This result is know n as Cantor’s theorem. [Hint: Suppose such a function f existed. Let T = {s ? S | s? f{s)) and show that no element s can exist for which f(s) = T.]

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QUESTION:

Show that if S is a set, then there does not exist an onto function f from S to the power set of 5. Conclude that |S|< This result is know n as Cantor’s theorem. [Hint: Suppose such a function f existed. Let T = {s ? S | s? f{s)) and show that no element s can exist for which f(s) = T.]

ANSWER:

Solution:Step 1 :In this problem we have to prove that if is a set, then there does not exist a

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