# Geometry: Inductive and Deductive Reasoning

## Contents

#### Problems

Problem : Take the following scenario: Every time a batter reaches first base, the next batter hits a double. Every time a batter hits a double, the runner on first scores. Jon reaches first base. What can you deduce about Jon?

Jon scores.

Problem : Take the following scenario: When the sun shines, the grass grows. When the grass grows, it needs to be cut. The sun shines. What can you deduce about the grass?

It needs to be cut.

Problem : Take the following scenario: Jim is a barber. Everybody who gets his hair cut by Jim gets a good haircut. Austin got a good haircut. What can you deduce about Austin?

Nothing. Just because Austin got a good haircut does not mean that Jim cut his hair. This is always possible, but nothing can be deduced from the situation.

Problem : All dogs are mammals, and all mammals are vertebrates. Shaggy is a dog. What can be deduced about shaggy?

Shaggy is a mammal and a vertebrate.

Problem : Why is the following example of deductive reasoning faulty? Given: Khaki pants are comfortable. Comfortable pants are expensive. Adrian's pants are not khaki pants. Deduction: Adrian's pants are not expensive.

Simply because Adrian's pants are not khaki does not mean that they are not comfortable. Also, even if they are not comfortable, this would not necessarily mean that they are not expensive. There could be comfortable pants that are not khakis, and expensive pants that are not comfortable.