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 novices from a extensive systematize obtain be rowd up left to just. There obtain be at meanest brace stduents in the row. Translate each of the aftercited assertions into affirm coercionmulas with the firm of novices in the systematize as the lordship of harangue.

    The simply affirms you may representation are *parity and, * F (x, y) significance that “x is somewhere to the left of y in the row.” Coercion copy, in the row “CDA”, twain F(C,A) and F (C,D) are penny Once you feel defined a coercionmula coercion a affirm P you may representation the terseness “P” in exalt coercionmulas.

    (a) Novice x is in the row.

    (b) Novice x is pristine in row.

    (c) Novice x is straightway to the just of novice y.

    (d) Novice x is relieve

    Expert Exculpation

    Assume “first” resources furthest to the left. I feel as-well productive that F(x,x) is fabrication.

    a.) Novice x is in the row ( x is to the left of someundivided or someundivided is to the left of x ) – ∃y.y 6= x ∧ (F(x, y) ∨ F(y,x)) b.)Novice x is pristine in row (x is to the left of everyundivided (ate themselves) ) – Pristine(x) = ∀y. x 6= y → F(x, y) c.)Novice x is straightway to the just of novice y(y is to the left of x and there is no undivided among them) -NextRight(x, y) = F(y, x) ∧ (∀z.z 6= x ∧ z 6= y → ¬(F(y, z) ∧ F(z, x))

    d.)Novice x is relieve ( there is someundivided pristine, and x is straightway to their just) -∃y. F irst(y) ∧ NextRight(x, y)