DEDUCTIVE REASONING

Deductive Reasoning

Definition Of Deductive Reasoning

When we arrive at a conclusion using facts, definitions, rule, or properties, it is called Deductive Reasoning.

More About Deductive Reasoning

A conclusion reached based on deductive reasoning is always true.

Video Examples: Deductive Reasoning

Solved Example on Deductive Reasoning

Ques: Is (x × y) × z the same as (z × y) × x always? Say yes or no. Explain your steps using deductive reasoning.

Choices:

A. Yes
B. No
Correct Answer: A

Solution:

Step 1: (x × y) × z = z × (x × y), using commutative property of multiplication.
Step 2: = z × (y × x), using commutative property of multiplication again.
Step 3: = (z × y) × x, using associative property of multiplication.

Quick Summary

Deductive reasoning uses general principles to reach specific conclusions.
The conclusion is always true if the premises are true.

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🍎 Teacher Insights

Emphasize the importance of verifying the premises before applying deductive reasoning. Use real-world examples to illustrate the concepts.

🎓 Prerequisites

Basic Algebra
Understanding of Mathematical Properties

Check Your Knowledge

Q1: Which of the following is an example of deductive reasoning?

A. All swans I have seen are white, therefore all swans are white. B. If all men are mortal, and Socrates is a man, then Socrates is mortal. C. Every time I kick a ball up, it comes back down, so gravity must exist. D. I get sleepy every time I eat bread, so bread must make people sleepy.

Frequently Asked Questions

Q: How does deductive reasoning differ from inductive reasoning?
A: Deductive reasoning goes from general to specific, guaranteeing the conclusion. Inductive reasoning goes from specific to general, and the conclusion is probable, not guaranteed.