8th grade Q2

Deductive reasoning is a way of thinking where you start with a general rule or principle and apply it to specific cases to reach a conclusion. It’s like following a set of instructions to solve a problem step by step.

How Deductive Reasoning Works:

1. Start with a General Rule: Use a statement or principle that is known to be true.
2. Apply the Rule to a Specific Case: Use the rule to analyze a particular situation.
3. Draw a Conclusion: Based on the application, reach a definite conclusion.

Example 1:

General Rule: All mammals have lungs.
Specific Case: A dog is a mammal.
Conclusion: Therefore, a dog has lungs.

Here, the general rule applies to the specific case of a dog, leading to a logically sound conclusion.

Example 2:

General Rule: If a number is even, it is divisible by 2.
Specific Case: The number 8 is even.
Conclusion: Therefore, 8 is divisible by 2.

You can verify this by dividing $8÷2=4$, which is a whole number.

Using Deductive Reasoning in Proofs:

In mathematics, deductive reasoning is often used in proofs. For example:

General Rule: For any two numbers $a$ and $b$, if $a=b$, then $a+c=b+c$ for any number $c$.
Specific Case: Let $a=5$, $b=5$, and $c=3$.
Conclusion: $5+3=5+3$ or $8=8$.

This conclusion is guaranteed to be true because it follows directly from the general rule.

Strengths of Deductive Reasoning:

Deductive reasoning always leads to a true conclusion as long as the general rule and specific case are correct.