Predicate Logic Evaluator

Satisfaction Ratio is calculated as satisfying elements divided by domain size before the calculator's logic ever branches on which quantifier you chose — it's a plain fraction, not a quantified truth value. The Quantifier only determines the separate Truth Value output, which applies a completely different rule (all, at least one, exactly one, or at least one false) depending on which option is selected.

At the calculator's defaults, it's actually a Math.round() artifact rather than a real difference in pull. A ten percent nudge on Elements Satisfying P(x) (default 7) lands on 7.7 or 6.3, and rounding to the nearest whole element inflates that to a full ±1, or about ±14.3% — bigger than the ten percent the nudge was meant to represent. Domain Size (default 10) doesn't get that same boost, since a ten percent nudge lands on 11 or 9, both already whole numbers with nothing for rounding to distort. Compare the two inputs without that rounding quirk and Domain Size actually edges out Elements Satisfying P(x) narrowly (about 0.202 versus 0.200) — the satisfying-count's apparent lead comes from which input's nudge happens to round further from its starting value, not from any inherent asymmetry between numerator and denominator.

Existential (there exists) is true as soon as at least one domain element satisfies the predicate, no matter how many others also do. Unique Existential is far stricter — it's only true when the count of satisfying elements equals exactly 1, so a predicate satisfied by two or more elements makes Unique Existential false even though ordinary Existential would still read true.

No — it's a statistical estimate, not a count of anything the calculator has actually verified. It multiplies the domain size squared by the Satisfaction Ratio squared, which assumes satisfaction is independent across every pair of elements; a real predicate where satisfaction clusters together or excludes certain pairs can produce a true pair count well above or below this estimate.