Question

If $P(n)$ is a statement such that $P(3)$ is true. Assuming $P(k)$ is true $\Rightarrow P(k+1)$ is true for all $k \ge 3$, then $P(n)$ is true

• A. for all $n$
• B. for $n \ge 3$
• C. for $n \ge 4$
• D. None of these

Hint:

Mathematical induction proves statements for all integers greater than or equal to the base case.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Mathematical induction principle.
Step 2: Detailed Explanation:
We have base case $P(3)$ true. The induction step holds for all $k \ge 3$. So by induction, $P(n)$ is true for all $n \ge 3$.
Step 3: Final Answer:
$P(n)$ is true for $n \ge 3$.