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Calcimator

Logical Equivalence Checker

Test whether two propositional logic expressions produce identical truth values across all variable assignments.

Inputs

Results

Equivalent (1=Yes)

0

Matching Rows

0

Different Rows4
Match Percentage0%
True Count (Expr 1)1
True Count (Expr 2)3
Total Rows4
How to Use This Calculator
  1. Enter two logical expressions using standard propositional logic notation.
  2. Assign truth values to each variable and evaluate both expressions.
  3. Review the truth table output showing both expressions' values at every input combination.
  4. If the truth values match for all inputs, the expressions are logically equivalent.
  5. Use the equivalence check to simplify complex propositions in proofs or circuit design.

How the result changes with Expression 2 (1=AND, 2=OR, 3=XOR, 4=IMPLIES, 5=NAND)

Expression 2 (1=AND, 2=OR, 3=XOR, 4=IMPLIES, 5=NAND)Equivalent (1=Yes)Matching Rows
1.414
2.402
3.602
4.600

What each input means

Expression 1 (1=AND, 2=OR, 3=XOR, 4=IMPLIES, 5=NAND)
Logical operation for the first expression
Expression 2 (1=AND, 2=OR, 3=XOR, 4=IMPLIES, 5=NAND)
Logical operation for the second expression
Number of Variables
Number of propositional variables shared between both expressions

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    Expression 1 (1=AND, 2=OR, 3=XOR, 4=IMPLIES, 5=NAND) = 1, Expression 2 (1=AND, 2=OR, 3=XOR, 4=IMPLIES, 5=NAND) = 5, Number of Variables = 2 = 3 input(s) provided
  2. Calculate Equivalent
    Equivalent
    0 = 0
  3. Calculate Matching Rows
    Matching Rows
    0 = 0
  4. Calculate Different Rows
    Different Rows
    4 = 4
  5. Calculate Match Percentage
    Match Percentage
    0 = 0

Engine last updated . Checked against 5 independently-derived tests — how we verify calculators.

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