Logical Equivalence Checker

Check if two logical expressions are equivalent by comparing their truth tables and simplified forms.

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About This Tool

This Logical Equivalence Checker tool allows you to input two logical expressions using standard operators (AND, OR, NOT, IMPLIES, XOR) and variables (single letters). The tool parses both expressions, generates complete truth tables for all variable combinations, and determines if the expressions are logically equivalent. It displays side-by-side truth tables, shows the equivalence result, and provides simplified expressions using basic laws. All processing happens client-side with no server required.

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How to Use

Enter your first logical expression in the left text area (e.g., '(p AND q) OR NOT r')
Enter your second logical expression in the right text area (e.g., 'NOT(NOT p OR NOT q) OR NOT r')
Select logical operators from the dropdown if needed (default includes AND, OR, NOT, IMPLIES, XOR)
Click the 'Check Equivalence' button to process
View the results showing whether expressions are equivalent, with truth tables and simplified forms

Frequently Asked Questions

Find Quick Answers

What logical operators are supported?

The tool supports AND, OR, NOT, IMPLIES (→), and XOR operators. You can use symbols (∧, ∨, ¬, →, ⊕) or words (AND, OR, NOT, IMPLIES, XOR).

How many variables can I use?

You can use up to 4 different variables (single letters like p, q, r, s) to keep truth tables manageable. More variables would make the table too large for display.

Does this tool require an internet connection?

No, all processing happens in your browser using JavaScript. No data is sent to any server.

What if my expressions have syntax errors?

The tool validates expressions and shows specific error messages highlighting problematic parts with suggestions for correction.

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