Calculator
Example Data Table
| Expression | P | Q | R | Result |
|---|---|---|---|---|
| (P AND Q) IMPLIES R | T | T | F | F |
| (P AND Q) IMPLIES R | T | F | F | T |
| (P AND Q) IMPLIES R | F | T | T | T |
Formula Used
This calculator evaluates each row by applying standard propositional logic rules. It converts the expression to postfix form, then computes one final truth value per row.
| Operator | Meaning | Rule |
|---|---|---|
| NOT P | Negation | True when P is false. |
| P AND Q | Conjunction | True only when both are true. |
| P OR Q | Disjunction | True when at least one is true. |
| P XOR Q | Exclusive OR | True when exactly one is true. |
| P NAND Q | Negated AND | NOT (P AND Q). |
| P NOR Q | Negated OR | NOT (P OR Q). |
| P IMPLIES Q | Conditional | Equivalent to NOT P OR Q. |
| P IFF Q | Biconditional | True when both values match. |
How to Use This Calculator
- Select how many variables you want to use.
- Enter a logical expression with P, Q, R, S, or T.
- Use parentheses to control grouping when needed.
- Click the generate button to build the full truth table.
- Review the summary, classification, PDNF, and PCNF output.
- Download the results as CSV or PDF for later use.
Logical Operations and Truth Tables Guide
Why this calculator helps
Logical operations support many math and computing tasks. Students use them in discrete mathematics. Developers use them in Boolean logic and conditions. This calculator makes evaluation easier. It removes manual errors. It also saves time during homework and revision.
What the tool can evaluate
You can test simple and complex expressions. The calculator supports NOT, AND, OR, XOR, NAND, NOR, IMPLIES, and IFF. You can also combine parentheses with up to five variables. That makes it useful for proofs, circuit logic, and symbolic reasoning.
How the truth table is built
A truth table lists every possible variable combination. If you choose three variables, the table shows eight rows. Four variables produce sixteen rows. Each row is tested against the same expression. The final column shows whether the expression is true or false for that case.
Why classification matters
The calculator labels the result as a tautology, contradiction, or contingency. A tautology is always true. A contradiction is always false. A contingency changes with input values. This helps you understand whether a statement is universally valid, impossible, or conditional.
Canonical forms made simple
The output also shows PDNF and PCNF forms. These are canonical logic representations. PDNF joins all true-result minterms. PCNF joins all false-result maxterms. These forms help in theorem work, switching design, and expression simplification tasks.
Useful for study and problem solving
This page is practical for classroom practice and exam review. It is also useful when checking implication chains and equivalence statements. Because the results can be exported, you can save tables for notes, handouts, and assignments. That makes the calculator helpful for repeated logic work.
FAQs
1. What does this calculator do?
It evaluates logical expressions and creates a full truth table. It also shows canonical forms, true rows, false rows, satisfiability, validity, and the final statement classification.
2. Which operators can I use?
You can use NOT, AND, OR, XOR, NAND, NOR, IMPLIES, and IFF. Parentheses are supported too. These options cover common propositional logic problems.
3. How many variables are supported?
You can work with one to five variables. The active variables are P, Q, R, S, and T, based on the number selected in the form.
4. What is a tautology?
A tautology is a statement that stays true for every possible row in the truth table. It represents a universally valid logical form.
5. What is a contradiction?
A contradiction is a statement that stays false for every row. It never becomes true, no matter how the variables are assigned.
6. Why are PDNF and PCNF included?
They show canonical forms of the final result. These forms help with simplification, proof steps, circuit design, and formal logic study.
7. Can I download the result?
Yes. After generating the truth table, you can export the displayed results as a CSV file or as a PDF report.
8. Why is implication true when the first part is false?
In formal logic, P IMPLIES Q is false only when P is true and Q is false. Every other combination counts as true.