Proof:
For all n∈N, let P(n) be the proposition:
|A|=n⟹|P(A)|=2n
where P(A) is the powerset of A
Basis for the Induction:
Induction Hypothesis:
We need to show that, if P(k) is true, where k≥2, then it logically follows that P(k+1) is true. So if this is our Induction Hypothesis:
|A|=k⟹|P(A)|=2k
We need to show that:
|A|=k+1⟹|P(A)|=2k+1
Induction Step:
18. Use induction to prove the following: For any set A, if IA] = n for...
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2: Use mathematical induction to prove that for any odd integer n >= 1, 4 divides 3n + 1 ====== Please type / write clearly. Thank you, and I will thumbs up!
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