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

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 infinite subset) to show that, if A is an infinite set, P(A) is uncountable.

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Expert Solution

Colby Messinger answered 1 year ago

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