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 k5 ∈ N and also proved that P(5) is true. On the basis of this, he could conclude that P(n) is true

Question

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 proved that P(5) is true. On the basis of this, he could conclude that P(n) is true (A) for all n ∈ N (B) for all n>5 (C) for all n ≥ 5 (D) for all n<5

Tardigrade Admin · Accepted Answer

Since, P(5) is true and P(k+1) is true, whenever P(k) is true.

Q. 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 $k > 5 \in N$ and also proved that $P (5)$ is true. On the basis of this, he could conclude that $P (n)$ is true

for all $n \in N$

for all $n > 5$

for all $n \geq 5$

for all $n < 5$

Since, $P (5)$ is true and $P (k + 1)$ is true, whenever $P (k)$ is true.

Q. 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 proved that P(5) is true. On the basis of this, he could conclude that P(n) is true

for all n∈N

for all n>5

for all n≥5

for all n<5