What is a Logical Argument?

A logical argument consists of premises (statements assumed to be true) and a conclusion (what follows from those premises). Your task is to evaluate whether the argument's structure is valid (the conclusion must follow from the premises) or invalid (the conclusion does not necessarily follow).

Reading Symbolic Logic

Symbolic logic uses letters and symbols to represent logical statements. Here are the basic symbols you'll encounter:

• P, Q, R = Variables representing statements
• → = "If... then..." (conditional)
• ∧ = "AND" (conjunction)
• ∨ = "OR" (disjunction)
• ¬ = "NOT" (negation)
• ↔ = "If and only if" (biconditional)
• ∴ = "Therefore" (marks the conclusion)

Example 1: Working Through Symbolic Logic

Let's analyze this symbolic argument:

How to evaluate it:

• Statement 1 says: "If P is true, then Q is true"
• Statement 2 says: "P is true"
• So Q must be true
• This is VALID (conclusion follows from the premises)

Example 2: Working Through Natural Language

Now let's examine the same argument in natural language:

How to evaluate it:

• Premise 1 tells us the relationship: rain → wet ground
• Premise 2 tells us the condition is met: it IS raining
• Conclusion follows logically: the ground MUST be wet
• This is VALID

Example 3: An Invalid Argument

Here's an example where the conclusion does NOT necessarily follow:

Why is this invalid?

• The ground could be wet for other reasons (sprinkler, snow melting, etc.)
• The premises don't guarantee that rain is the ONLY way the ground gets wet
• So the conclusion doesn't necessarily follow
• This is INVALID

How to Use This App

Start with the Tutorial: Get the core ideas of validity, structure, and evaluation before you jump into practice.

Work through Lessons: Use the Logic Lessons page to move step-by-step from the Pre-Module through Lesson 9. Each lesson combines explanations with quizzes and activities.

Practice Modes: Choose Symbolic or Natural Language practice to train different skills. Use Mixed Mode to practice both. Use Timed Mode for a fast, score-based challenge.

Reference & Dictionary: The Argument Forms Reference shows standard valid and invalid forms. The Logic Dictionary defines key terms and concepts.

Insights & Progress: Check the Insights page to track accuracy, streaks, and your weakest forms. Progress is saved locally on your device.

Quick Checklist for Evaluating Arguments

• ✓ Identify all premises (what's given as true)
• ✓ Identify the conclusion (what's being claimed to follow)
• ✓ Ask: "If all premises are true, must the conclusion be true?"
• ✓ If YES → the argument is VALID
• ✓ If NO (you can find a counterexample) → the argument is INVALID