Understand the subject
What is logical equivalence?
Two propositions are logically equivalent when they have exactly the same truth value on every possible valuation.
Use it to verify a rewrite without relying on how similar two expressions look.
See the structure
What the rule checks
T T → TT F → FF T → TF F → T
F≡G iff F and G agree on every valuation.Worked interpretation
Read the result in context
P→Q and ¬P∨Q agree on all four rows.
Interpret with care
Important boundary
Matching on a few chosen examples is not enough; every truth-table row matters.
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
F≡G iff F and G agree for every valuation.
The calculator validates the mathematical domain before returning a result and does not replace undefined states with zero.
Worked example
Worked example
P -> Q is equivalent to !P | Q.
F≡G iff F and G agree for every valuation.
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.
