Understand the subject
What does a truth table do?
A truth table lists every possible truth-value assignment and evaluates a proposition row by row.
Use it to distinguish a tautology, contradiction, and contingent statement.
See the structure
What the rule checks
T T → TT F → FF T → TF F → T
P→Q is false only when P is true and Q is false.Worked interpretation
Read the result in context
P→Q is equivalent to ¬P∨Q on every row.
Interpret with care
Important boundary
The number of rows doubles with every new proposition, so large expressions become impractical.
Use the Set Operations Calculator to explore small finite examples.
Quick guide
How to use this calculator
- Enter values using the notation shown beside each field.
- Choose a calculation mode when the tool offers more than one interpretation.
- Read the primary answer first, then inspect the supporting details.
Calculation method
Apply the stated definition
Operators: !, &, |, ^, ->, <->
The calculator validates the mathematical domain before returning a result and does not replace undefined states with zero.
Worked example
Worked example
(P -> Q) <-> (!P | Q) is a tautology.
Operators: !, &, |, ^, ->, <->
Supported inputs
Precision and limits
Finite, bounded input
Set and logic tools use finite inputs so every result can be checked completely. Each page states its practical size limit.
Notation
Set elements are comma-separated text labels. Logic operators and relation-pair notation are documented in the relevant input labels.
