Changing subject to negative of predicate and predicate to negative of subject can make new statements {contrapositive}| {transposition, logic} {contraposition}. "If A then B" transposes to "If not B, then not A". If theorem is true, contrapositive is true. If contrapositive is true, theorem is true. "All A are B" transposes to "All not B are not A". "Some A are not B" transposes to "Some B are not A". "No A are B" transposes to "No not B are not A". "Some A are B" transposes to "Some not B are not A". For true statements, contrapositive of "All A are B" and "Some A are not B" are true. For true statements A and B, "No A are B" and "Some A are B" contrapositives are not true.
Mathematical Sciences>Logic>Statements>Permutations
3-Logic-Statements-Permutations
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Date Modified: 2022.0224