Question 15: Part a: Find f(3) for a function f(n) defined recursively: f(0)=1 f(n+1)=f(n)^2- f(n)+1 Write your answer b

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Question 15:
Part a:
Find f(3) for a function f(n) defined recursively:
f(0)=1
f(n+1)=f(n)^2- f(n)+1
Write your answer below:
Part b:
Find f(3) for a function f(n) defined recursively:
f(0)=1
f(n+1)=2^f(n)-1
Write your answer below:
Part c:
Find f(4) for a function f(n) defined recursively:
f(0)=1
f(1)=3
f(n+1)=f(n)f(n-1)
Write your answer below:
Part d:
Define a set A of strings of alphabet {0, 1} as below:
λ∈A,λ∈A, where λλ is an empty string
1x0∈A1x0∈A, if x∈Ax∈A.
Claim: any string in A has k 1s followed by k 0s, for a
non-negative integer k.
Group of answer choices
True
False
Please answer all parts with full work shown, thank you!