The question asks for the first step in mathematical induction. The answer choices are: a) Induction step, b) Hypothesis step, c) Basis step, d) None of the above, e) Conclusion step.

1. Problem Description

The question asks for the first step in mathematical induction. The answer choices are: a) Induction step, b) Hypothesis step, c) Basis step, d) None of the above, e) Conclusion step.

2. Solution Steps

Mathematical induction is a method of proving a statement for all natural numbers. The steps involved in mathematical induction are:

1. Basis step: Prove the statement is true for the base case (usually $n=0$ or $n=1$).

2. Inductive hypothesis: Assume the statement is true for some arbitrary natural number $k$.

3. Inductive step: Prove the statement is true for $k+1$, using the assumption that it is true for $k$.

4. Conclusion step: Conclude that the statement is true for all natural numbers $n$.

The first step in mathematical induction is the basis step.

3. Final Answer

c. Basis step