Traditional logic used relations {square of opposition} between the four proposition forms to show inferences, contradictions, and contraries.
four forms
All a are b. No a are b. Some a are b. Some a are not b.
contraries
"All a are b" and "No a are b" are contraries, because both can be false and both cannot be true {contrary relation}.
"Some a are b" and "Some a are not b" are subcontraries, because both can be true and both cannot be false {subcontrary relation}.
contradiction
"All a are b" and "Some a are not b" are contradictories, because one must be true and one must be false {contradictory relation}. "No a are b" and "Some a are b" are contradictories, because one must be true and one must be false.
subalternation
"All a are b" entails "Some a are b" {subalternation relation}. "No a are b" entails "Some a are not b".
Mathematical Sciences>Logic>Reasoning
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Date Modified: 2022.0224