# Deductive Argument: Definition & Examples

Instructor: Beverly Maitland-Frett

Beverly has taught mathematics at the high school level and has a doctorate in teaching and learning.

Intentionally or unintentionally, we reason deductively. In this lesson, we will examine the definition of deductive arguments, look at some uses and explore some examples of ways in which we reason or argue deductively.

## Definition of Deductive Reasoning

Everyday we reason deductively. This just means that we use facts that we already know to build on other facts until we come to a desired conclusion. For example, Sully spent some time in a major mall. Now it's time for her to go home, but she forgot where she parked her car. She knows that her car is blue, fact number 1. She also knows that her make is Honda, fact number 2. She remember that she parked between section E and D. So, what can she do? Of course, she is going to check all the blue Hondas in section E until she identifies her car. That is what deductive reasoning is about. You use your general knowledge about something to arrive at a specific conclusion.

### Definition of Deductive Argument

An argument begins with a statement that we believe to be true or false, which we call the premise. Then we reason in a logical manner to arrive at a conclusion. A deductive argument is a type of logical argument that begins with a factual premise such that the conclusion you want to reach must be true. It uses deductive reasoning to arrive at a conclusion. Sully used the general factual premise that she drives a blue Honda to search for her specific car. Had she started searching for a red Honda, she would have never found her car. She began with facts about her car and, ultimately, will have to find her car. Therefore, a deductive argument begins with a known fact that will ultimately lead to conclusion that is true. Remember, with deductive reasoning, you will undoubtedly arrive at a true conclusion. If you don't, then you didn't begin with a factual statement.

## Uses of Deductive Arguments

Deductive arguments are used mainly in mathematics, sciences, and philosophical debates. In mathematics, deductive arguments are used to derive mathematical theorems and formulas, and in geometrical proofs. In sciences, these arguments help to make conclusions about human, plant and animal development, as well as the prevention and cure of diseases. Plus, as mentioned earlier, we constantly use deductive reasoning without knowing it.

## Examples of Deductive Arguments

We will explore some mathematical arguments.

Example 1: Use deductive reasoning to prove that a quadrilateral is a polygon.

A polygon is a closed figure having three or more sides. This is the general factual premise that we will start with. Another fact we know is that a quadrilateral is a four-sided closed figure. Since a quadrilateral is a four-sided closed figure, and four is more than three, then a quadrilateral must be a polygon.

Example 2: Let's examine a two column geometric proof.

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