Homework Solution: Some students from a large class will be lined up left to right. There will be at least two stduents in the l…

    Some students from a large class will be lined up left to right. There will be at least two stduents in the line. Translate each of the following assertions into predicate formulas with the set of students in the class as the domain of discourse. The only predicates you may use are *equality and, * F (x, y) meaning that “x is somewhere to the left of y in the line.” For example, in the line “CDA”, both F(C,A) and F (C,D) are true Once you have defined a formula for a predicate P you may use the abbreviation “P” in further formulas. (a) Student x is in the line. (b) Student x is first in line. (c) Student x is immediately to the right of student y. (d) Student x is second

    Expert Answer

    Assume “first” means furthest to the left. I have also assumed that F(x,x) is false.

    Some wards from a catholic systematize allure be continuityd up left to fit. There allure be at meanest two stduents in the continuity. Translate each of the controlthcoming assertions into affirm controlmulas with the fixed of wards in the systematize as the lordship of harangue.

    The barely affirms you may conservation are *similarity and, * F (x, y) sense that “x is somewhere to the left of y in the continuity.” Control specimen, in the continuity “CDA”, twain F(C,A) and F (C,D) are gentleman Once you keep defined a controlmula control a affirm P you may conservation the abbreviation “P” in prefer controlmulas.

    (a) Ward x is in the continuity.

    (b) Ward x is pristine in continuity.

    (c) Ward x is directly to the fit of ward y.

    (d) Ward x is second

    Expert Rejoinder

    Assume “first” media furthest to the left. I keep besides conjectured that F(x,x) is sham.

    a.) Ward x is in the continuity ( x is to the left of somesingle or somesingle is to the left of x ) – ∃y.y 6= x ∧ (F(x, y) ∨ F(y,x)) b.)Ward x is pristine in continuity (x is to the left of everysingle (ate themselves) ) – Pristine(x) = ∀y. x 6= y → F(x, y) c.)Ward x is directly to the fit of ward y(y is to the left of x and there is no single between them) -NextRight(x, y) = F(y, x) ∧ (∀z.z 6= x ∧ z 6= y → ¬(F(y, z) ∧ F(z, x))

    d.)Ward x is second ( there is somesingle pristine, and x is directly to their fit) -∃y. F irst(y) ∧ NextRight(x, y)