1)Show that a subset of a countable set is also countable. 2) Let P(n) be the...

1)Show that a subset of a countable set is also countable.

2) Let P(n) be the statement that 13 + 23 +· · ·+n3 =(n(n + 1)/2)2 for the positive integer n.

a) What is the statement P(1)?

b) Show that P(1) is true, completing the basis step of

the proof.

c) What is the inductive hypothesis?

d) What do you need to prove in the inductive step?

e) Complete the inductive step, identifying where you

use the inductive hypothesis.

f ) Explain why these steps show that this formula is true

whenever n is a positive integer.

Expert Solution

Thankue

Colby Messinger answered 2 years ago

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