Question

Explain the purposes of inductive and deductive reasoning in mathematics. Be sure to define both inductive reasoning and deductive reasoning and describe how each can help you develop and prove theorems.

Answer 1

When it comes to deductive reasoning, it is used to reach a logical solution. You start out with the general statement, or hypothesis, and examine all the possibilities so you can reach the final conclusion.

Inductive reasoning is completely opposite - you focus on specific observations, and then make broad generalizations.  

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Answer 2

Inductive reasoning is used when finding or forming a conjecture. 
Deductive reasoning is used to prove a conjecture. 
In math we usually start with a conjecture and then prove it using deductive reasoning.