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Recall that in class we defined, for any set A, P(A) := {B : B...

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Advance Math

Recall that in class we defined, for any set A, P(A) := {B : B ?A}, which we called the power set of A.

a) (10) Show that, if a set A has n elements (where n ? {0, 1,2, 3, 4, . . .}), P(A) has exactly 2 n elements.

b) (10) Use #4(any infinite set S has a countably infinitesubset) to show that, if A is an infinite set, P(A) isuncountable.

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