Understanding Logical Equivalence
Logical equivalence means two statements always share the same truth value. They may look different. They still say the same thing in every possible case. This calculator checks that idea by building a complete truth table.
Why Truth Tables Matter
A truth table lists every possible assignment for the variables used in both formulas. For each row, the tool evaluates the left expression and the right expression. If both final columns match on all rows, the formulas are equivalent. If one row differs, they are not equivalent.
What The Tool Solves
The calculator accepts common symbols and plain text operators. You may type not, and, or, xor, implies, and biconditional forms. It also supports compact symbols like !, &, |, ->, and <->. Parentheses control grouping. This makes the tool useful for class work, digital logic, and proof checking.
Step Based Evaluation
Each row includes a short step trail. The trail shows variable values first. Then it shows how inner parts are evaluated. Finally, it compares both complete formulas. These steps help you find exactly where two expressions agree or fail.
Useful Study Features
The result panel gives the verdict first, so the answer is easy to see. The full table follows below. You can also download the table as a CSV file. A simple PDF report is available for notes or submission. These exports help keep work organized.
Good Formula Habits
Use clear variable names. Keep parentheses around important groups. Write implications with ->. Write biconditionals with <->. Check one idea at a time when a formula becomes long. Smaller formulas are easier to debug.
Practical Examples
A classic equivalence is p -> q and !p | q. Another common law is !(p & q) and !p | !q. These are not just symbolic tricks. They explain how conditions, switches, rules, and permissions can be rewritten safely.
Final Note
Logical equivalence is a strict test. Matching most rows is not enough. The formulas must match every row. Use the steps and table together for the clearest proof. Review exported results before sharing them. Small typing errors can change a whole proof. Try replacing rare symbols with text operators when needed. Save examples that helped you understand a rule, especially during exams too.