# How to Reason Deductively From a Set of Statements

Instructor: Benjamin Truitt
In this lesson, you will learn that deductive reasoning is a very useful skill to have in a variety of scenarios. Deductive reasoning requires applying the rule of non-contradiction to a case to determine what conclusions can be logically determined.

## How to Reason Deductively from a Set of Statements

'Elementary my dear Watson!' Sherlock Holmes would proclaim after solving another mystery. Holmes would then proceed to explain how he had figured out through logic the way the crime had been committed. This process of working out what must be true from the facts of a case is deductive reasoning. So, how can you reason like Sherlock Holmes when facing a conundrum?

## Deductive Process

If you are given a set of facts about a case like Sherlock Holmes, deduction is the process where you examine the relationships of those facts and figure out what else must be true. Deduction occurs when we apply the law of non-contradiction to problems of categories, if/then claims, or the application of rules. The law of non-contradiction is that a thing cannot be and not be at the same time. This rule, when applied to a series of statements, tells us whether or not a conclusion is true, unknown, or false. For example, if we reason about categories:

(a) All men are mortal.

(b) Socrates is a man.

(c) Therefore, Socrates is mortal.

This argument (or syllogism) tells us that if we know (a) and (b), then we know (c) because the opposite conclusion (Socrates is immortal) would contradict the first two statements. Here is another example using if/then statements:

(a) If you poke a bear,

(b) Then, he will be mad.

If you do poke the bear, then you know from these facts that the bear will be mad. If you poke the bear, and he is not mad, it exposes a contradiction, revealing that one or both of these statements is wrong.

## Methods for Approaching Deductive Problems

Well, now that we know you should not poke Socrates, and that bears are mortal, we now should discuss how you can use these skills in life and what methods you can use to solve deductive problems. Outside of mental exercises and solving murder-mysteries, when can you use deductive reasoning? There are actually many cases where you can use it! Professionals use deductive reasoning to solve problems like scheduling employees for shifts, prioritizing tasks, or determining who to give a grant to. Let's discuss some methods for solving a deductive issue.

We saw above how to solve simple examples; now, let's tackle one that is more complex. You need to put together a shift schedule for a week and have five employees. You only need two to work any given time, and there are some limitations you need to work around:

1. No employee can work more than three days in a week.

2. Employees Molly and Lisa can work on Wednesday or Friday, but not both due to other obligations.

3. Employee John can only work on Mondays and Fridays.

4. Employee Kevin cannot work with employee Lisa.

5. All the employees must work as many days as possible.

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