Question

Tell whether the reasoning process is deductive or inductive.

Linda observes that,${(-1)}^2=+1,{(-1)}^4=+1$ and ${(-1)}^6=+1$. She concludes that every even power of$(-1)$ is equal to +1.

Short answer

The reasoning process is inductive.

Step-by-step solution

Step 1. Define deductive reasoning

Deductive reasoning is conclusions based on accepted statements like a theorem, postulate, facts etc.

Step 2. Define inductive reasoning

Inductive reasoning is conclusions based on several past observations.

Step 3. State whether reasoning is inductive or deductive

From the given statement “Linda observes that, ${(-1)}^2=+1,{(-1)}^4=+1$and ${(-1)}^6=+1$. She concludes that every even power of $(-1)$is equal to +1.”, it is clear that the conclusion is based on several past observations. Thus, this conclusion is probably true but not necessarily true.

Therefore, the reasoning process is inductive.