Calculator Form
Formula Used
¬(A ∧ B) = ¬A ∨ ¬B
¬(A ∨ B) = ¬A ∧ ¬B
¬(A ∧ B ∧ C ∧ ...) = ¬A ∨ ¬B ∨ ¬C ∨ ...
¬(A ∨ B ∨ C ∨ ...) = ¬A ∧ ¬B ∧ ¬C ∧ ...
The calculator first evaluates the grouped inner statement. It then negates that result. Next, it builds the transformed expression by switching AND with OR and negating every individual term. The truth table confirms both expressions always match for every possible input row.
How to Use This Calculator
- Select the law type: negated AND group or negated OR group.
- Choose whether you want 2, 3, or 4 variables.
- Pick the value of each variable as True or False.
- Choose symbols or word notation for the displayed expressions.
- Press the calculate button to show the result above the form.
- Review the original expression, transformed expression, and equivalence check.
- Use the truth table and Plotly graph for deeper verification.
- Download the truth table as CSV or export the result as PDF.
Example Data Table
| Example | Expression | Values | Equivalent Form | Result |
|---|---|---|---|---|
| 1 | ¬(A ∧ B) | A=True, B=False | ¬A ∨ ¬B | True |
| 2 | ¬(A ∨ B) | A=False, B=False | ¬A ∧ ¬B | True |
| 3 | ¬(A ∧ B ∧ C) | A=True, B=True, C=False | ¬A ∨ ¬B ∨ ¬C | True |
| 4 | ¬(A ∨ B ∨ C) | A=False, B=True, C=False | ¬A ∧ ¬B ∧ ¬C | False |
| 5 | ¬(A ∧ B ∧ C ∧ D) | A=True, B=True, C=True, D=True | ¬A ∨ ¬B ∨ ¬C ∨ ¬D | False |
FAQs
1. What does this De Morgan's Law calculator do?
It transforms a negated AND or OR expression into its equivalent form, evaluates both versions, and proves equivalence through a full truth table.
2. What is De Morgan's first law?
The first law states that the negation of a conjunction becomes the disjunction of individual negations: ¬(A ∧ B) = ¬A ∨ ¬B.
3. What is De Morgan's second law?
The second law states that the negation of a disjunction becomes the conjunction of individual negations: ¬(A ∨ B) = ¬A ∧ ¬B.
4. Why do the original and transformed expressions match?
De Morgan's laws are logical identities. That means both forms produce identical outputs for every possible variable combination, which the truth table confirms.
5. Can I use more than two variables?
Yes. This version supports 2, 3, and 4 variables, and the generalized law applies the same operator switch and individual negation pattern.
6. What does the inner expression value mean?
It is the truth value of the grouped statement before the outer negation is applied. The calculator shows it to clarify each evaluation step.
7. What is the Plotly graph showing?
The graph compares how many truth-table rows evaluate to True or False for the original expression and its transformed equivalent.
8. Who should use this calculator?
It is useful for students, teachers, competitive exam preparation, discrete mathematics practice, computer science logic lessons, and proof checking.