Understanding De Morgan Law
De Morgan law explains how a negation moves across AND or OR. It is a core rule in logic, programming, digital circuits, and set theory. The rule says that not A and B equals not A or not B. It also says that not A or B equals not A and not B. This calculator shows both sides together, so you can see why the statements match.
Why This Rule Matters
The law helps simplify hard logic expressions. It also helps convert one circuit style into another. A programmer can use it to rewrite conditions with cleaner checks. A student can use it to test a proof before writing final steps. A designer can use it to replace a NAND structure with an OR of complements, or replace a NOR structure with an AND of complements. The idea is simple, but the effect is powerful.
Boolean and Set Support
This tool supports two common views. The Boolean view uses true and false values for A, B, and C. It compares the left expression with the transformed right expression. The set view uses a universe and two sets. It compares the complement of an intersection or union with the matching operation on complements. Both methods show the same pattern in different language.
Truth Table Use
A truth table is the strongest check for a small logic statement. It lists every possible value pattern. Then it evaluates each side. If every row gives the same answer, the two statements are equivalent. The table in this page can be exported for notes, reports, or classroom work.
Practical Tips
Use two variable mode for basic lessons. Use three variable mode for longer proofs. Keep set items short and unique. Enter comma separated values for clean exports. Review the step explanation before copying results. The calculator does not replace understanding. It gives a clear check, a formula view, and downloadable evidence. That makes it useful for learners, tutors, engineers, and anyone handling logical decisions.
Common Mistakes
Do not change both operators in the same direction. Negation flips AND to OR, and OR to AND. Also complement every included variable. Missing one complement creates a different statement during careful review sessions later.