If the first variable is universally quantified and the second is existentially quantified it translates as, “For all X, there is a Y (such that) X dislikes Y”. In English, “Everyone dislikes someone"...If the first variable is universally quantified and the second is existentially quantified it translates as, “For all X, there is a Y (such that) X dislikes Y”. In English, “Everyone dislikes someone". Let \(Q\) be the statement: For all real numbers \(a\) and \(b,\) if \(a+b\) is irrational or \(a-b\) is irrational then \(a\) is irrational and \(b\) is irrational.
This page discusses the enhancements of predicate logic over propositional logic, focusing on object properties and relationships using quantifiers. It explains translation of English statements into ...This page discusses the enhancements of predicate logic over propositional logic, focusing on object properties and relationships using quantifiers. It explains translation of English statements into predicate logic, clarifies common misconceptions about quantifiers, and emphasizes practical applications in fields like AI and mathematics. The text also includes exercises to practice translating statements, underscoring the importance of precision in logical understanding.