5. The predicate P(n) is defined to be the assertion that: n P(n) :Ej j! = (n+ 1)! – 1. %3D j=0 (a) Verify that P(4) is true. (b) Express P(k). (c) Express P(k + 1).

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5. The predicate P(n) is defined to be the assertion that:
n
Pin) : Σ)j1 (n+ 1)! - 1.
j=0
(a) Verify that P(4) is true.
(b) Express P(k).
(c) Express P(k+ 1).
(d) In an inductive proof that for all n > 1,
n
Ei j! = (n+ 1)! – 1
j=0
what must be proven in the base case?
(e) In an inductive proof that for all n > 1,
n
Ej j! = (n+ 1)! – 1
j=0
what must be proven in the inductive step?
(f) What would be the inductive hypothesis in the inductive step from your previous
answer?
(g) Prove by induction that for all n > 1,
Ej. j! = (n + 1)! – 1
j=0
Transcribed Image Text:5. The predicate P(n) is defined to be the assertion that: n Pin) : Σ)j1 (n+ 1)! - 1. j=0 (a) Verify that P(4) is true. (b) Express P(k). (c) Express P(k+ 1). (d) In an inductive proof that for all n > 1, n Ei j! = (n+ 1)! – 1 j=0 what must be proven in the base case? (e) In an inductive proof that for all n > 1, n Ej j! = (n+ 1)! – 1 j=0 what must be proven in the inductive step? (f) What would be the inductive hypothesis in the inductive step from your previous answer? (g) Prove by induction that for all n > 1, Ej. j! = (n + 1)! – 1 j=0
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