Master

Law of Detachment

Master law of detachment with interactive lessons and practice problems! Designed for students like you!

Learn

Get the basics

Practice

Apply your skills

Master

Achieve excellence

Law of Detachment

Study Guide

Key Definition

The Law of Detachment states that if the statements $p \to q$ and $p$ are true, then $q$ is also true.

Important Notes

If $p \to q$ is true and $p$ is true, then $q$ must be true.
This law is a fundamental rule in logical reasoning.
It is used to derive conclusions from known facts.
The statements must be factual for the law to apply.
This is different from the Law of Syllogism.

Mathematical Notation

$\to$ represents logical implication

$\land$ represents logical 'and'

$\lor$ represents logical 'or'

$\neg$ represents logical negation

$\forall$ represents 'for all'

Remember to use proper notation when solving problems

Why It Works

The Law of Detachment works because it follows the logical structure where if a condition is met, then a specific result follows. This is represented in formulas as $p \to q$.

Remember

Always ensure that the initial statements are true before applying the Law of Detachment. This is crucial for the validity of the conclusion.

Quick Reference

Implication:$p \to q$

Conclusion:$q$

Understanding Law of Detachment

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

The Law of Detachment allows us to conclude $q$ if $p \to q$ and $p$ are true.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

If it rains, the ground will be wet. It is raining. What can you conclude?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

If you finish your homework, you can play video games. You have finished your homework. What can you deduce?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If a number is even, then it is divisible by 2. Consider a number that is even. What can be deduced?

Challenge Quiz

Single Choice Quiz

Advanced

If $x \gt 5$, then $x^2 \gt 25$. $x \gt 5$. What follows?

Recap

Watch & Learn

Review key concepts and takeaways