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In the conceptual interpretation, when <math>a</math> and <math>b</math> denote concepts, the relation <math>a \in b</math> signifies that the concept <math>a</math> is subsumed under the concept <math>b</math>; that is, it is a species with respect to the genus <math>b</math>. From the extensive point of view, it denotes that the class of <math>a</math>'s is contained in the class of <math>b</math>'s or makes a part of it; or, more concisely, that "All <math>a</math>'s are <math>b</math>'s". From the comprehensive point of view it means that the concept <math>b</math> is contained in the concept <math>a</math> or makes a part of it, so that consequently the character <math>a</math> implies or involves the character <math>b</math>. Example: "All men are mortal"; "Man implies mortal"; "Who says man says mortal"; or, simply, "Man, therefore mortal".
In the propositional interpretation, when <math>a</math> and <math>b</math> denote propositions, the relation <math>a \Rightarrow b</math> signifies that the proposition <math>a</math> implies or involves the proposition <math>b</math>, which is often expressed by the hypothetical judgement, "If <math>a</math> is true, <math>b</math> is true"; or by "<math>a</math> implies <math>b</math>
''Remark''. -- Such a relation is a proposition, whatever may be the interpretation of the terms <math>a</math> and <math>b</math>.
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