McMaster UniversityDepartment of Computing and SoftwareDr. W. KahlCOMP SCI 1FC3Exercise Sheet 4COMP SCI 1FC3 — Mathematics for Computing1February 2009Exercise 4.1 — Predicates, formal and EnglishTranslate each of these formulae into an English statement that expresses a mathematical fact. The domain in eachcase consists of all real numbers.(a)∃x∀y(x+y=y)(b)∃x∀y(xy=y)(c)∃x∀y(yx=y)(d)∃x∀y(yx=x)(e)∀x∀y(((x≥ 0) ∧ (y≤ 0)) → (x-y> 0))(f)∃x∃y(((x≤ 0) ∧ (y≤ 0)) ∧ (x-y> 0))(g)∀x∀y((x=/ 0) ∧ (y=/ 0) ↔ (xy=/ 0))(h)∀x∀y∃z(x+y=z)Exercise 4.2 — Predicates, formal and EnglishUse quantifiers and predicates with more than one variable to express each of the following statements.(a)There is a student in this class who speaks Hindi.(b)Every student in this class plays some sport.(c)Some student in this class has visited Alaska but has not visited Hawaii.(d)Exactly one student in this class has visited Hawaii.
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