A student was asked to prove a statement P(n) by induction. He pr… - Vidyadip

MCQ

A student was asked to prove a statement P(n) by induction. He proved that P(k + 1) is true whenever P(k) is true for all k > 5 ∈ N and also that P(5) is true. Based on this, he could conclude that P(n) is true:

A
for all n ∈ N
B
for all n > 5
✓
for all n ≥ 5
D
for all n < 5

✓

Answer

Correct option: C.

for all n ≥ 5

The student could be able to conclude that P(n) is true for all n ≥ 5 since P(5) is true for all k > 5 ∈ N as well as true for P(5) and P(k + 1) is true, whenever P(k) is true.

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