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Let S be a statement of the form P implies Q (P → Q). Then the converse of S is the statement Q implies P (Q → P). In general, the truth of S says nothing about the truth of its converse, [2] unless the antecedent P and the consequent Q are logically equivalent. For example, consider the true statement "If I am a human, then I am mortal."
" In this case, unlike the last example, the inverse of the statement is true. The converse is "If a polygon has four sides, then it is a quadrilateral." Again, in this case, unlike the last example, the converse of the statement is true. The negation is "There is at least one quadrilateral that does not have four sides.
The converse relation does satisfy the (weaker) axioms of a semigroup with involution: () = and () =. [12] Since one may generally consider relations between different sets (which form a category rather than a monoid, namely the category of relations Rel ), in this context the converse relation conforms to the axioms of a dagger category (aka ...
In the universe of utterances there are statements S and questions Q. There are two relations π and α from Q to S: q α a holds when a is a direct answer to question q. The other relation, q π p holds when p is a presupposition of question q. The converse relation π T runs from S to Q so that the composition π T α is a homogeneous ...
Obversion changes the quality (that is the affirmativity or negativity) of the statement and the predicate term. [10] For example, by obversion, a universal affirmative statement become a universal negative statement with the predicate term that is the class complement of the predicate term of the original universal affirmative statement.
The <* is required for sets of numbers: If x is any real number, and { } is the null set, a<*{ } is taken to be a true statement. In other words, 3≥{ } cannot be true because it is meaningless to compare a number with a non-number. This permits us to define a modified "converse" statement 3<*{ } to be true!
Tara Stewart Kuhnen, director of GM corporate affairs, emailed a statement to the Detroit Free Press: “In order to win in this competitive market, we need to optimize for speed and excellence.
1 Statement. 2 Proof. 3 Example. 4 One-sided version. 5 Example. 6 Converse of the one-sided comparison test. 7 Example. ... Therefore, by the converse of the ...