Predicate Logic Evaluator

Evaluate quantified predicate logic statements (universal, existential, unique existential) over a finite domain.

Domain Size

Elements Satisfying P(x)

Quantifier (1=∀, 2=∃, 3=∃!, 4=¬∀)

Tab to move between fields

Truth Value (1=True)

Satisfaction Ratio

0.7

True Count7

False Count3

Counterexamples (∀)3

Witnesses (∃)0

Expected Satisfying Pairs (∀x∃y)49

Quantifier NameUniversal (∀)

How to Use This Calculator

Enter a predicate formula using quantifiers (∀, ∃) and logical connectives.
Define the domain of discourse and specify values for free variables.
Review the formula's truth evaluation over the specified domain.
Check for valid inferences by testing whether the conclusion follows from the premises.
Use the output to verify formal arguments in mathematics or computer science.

What each input means

Domain Size: Number of elements in the domain of discourse
Elements Satisfying P(x): How many domain elements make the predicate P true
Quantifier (1=∀, 2=∃, 3=∃!, 4=¬∀): 1=Universal(∀), 2=Existential(∃), 3=Unique Existential(∃!), 4=Negated Universal

Identify Input Parameters
Domain Size = 10, Elements Satisfying P(x) = 7, Quantifier (1=∀, 2=∃, 3=∃!, 4=¬∀) = 1 = 3 input(s) provided
Calculate Truth Value
0 = 0
Calculate Satisfaction Ratio
Satisfaction Ratio
0.7 = 0.7
Calculate True Count
True Count = 7
7 = 7
Calculate False Count
False Count
3 = 3

Engine last updated August 5, 2026. Checked against 4 independently-derived tests — how we verify calculators.

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