5. Consider the following definitions of predicates about football leagues. T(x)

Question

5. Consider the following definitions of predicates about football leagues. T(x): z is a football team. L(x): x is a football league. X (x, y, z): team r plays in league y in year z. P(z, z): z and a are teams that have played each other. A(z, y,2): team a wins league y in year z. translate the following statements (which may not be true) about football leagues into English. (24 marks) (a) Based on these definitions (and also using the predicate ii. Va. Vb. vc. Vd. (X(a, b, c) A X (a, b, d))-c-d vii. a binary predicate M is defined via the following M(x, y)Bu. : Vz. A(z, v, z) »-A(y,v, z) explain in English what relationship M expresses.

Explanation / Answer

(i) There exist teams x and y such that x and y have played each other.

(ii) For all x, if x is a football league then there exist team y and year z such that team y plays in league x in the year z.

(iii) For all teams a, all leagues b and all years c and d , if team x plays in league y in the year c and d then c equals to d.

(iv) There exists a league x, a league y, a year z and a team v such that team v is not played in leagues x and leagues y in the year z.

(v) same as (iv)

(vi) Either there exists a league x or there exist teams v and w that have not played each other.

(vii) M (x,y) means there exists a league v and a year z such that x wins the league v in year z if and only if team y does not wins the league v in year z.

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.