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 capacious adjust obtain be successiond up left to upright. There obtain be at last two stduents in the succession. Translate each of the restraintthcoming assertions into affirm restraintmulas with the restraintmal of novices in the adjust as the estate of yarn.

    The barely affirms you may fit are *similarity and, * F (x, y) import that “x is somewhere to the left of y in the succession.” Restraint issue, in the succession “CDA”, twain F(C,A) and F (C,D) are penny Once you feel defined a restraintmula restraint a affirm P you may fit the succinctness “P” in further restraintmulas.

    (a) Novice x is in the succession.

    (b) Novice x is foremost in succession.

    (c) Novice x is presently to the upupfit of novice y.

    (d) Novice x is assist

    Expert Retort

    Assume “first” resources furthest to the left. I feel besides antecedent that F(x,x) is falsity.

    a.) Novice x is in the succession ( x is to the left of someindividual or someindividual is to the left of x ) – ∃y.y 6= x ∧ (F(x, y) ∨ F(y,x)) b.)Novice x is foremost in succession (x is to the left of everyindividual (bar themselves) ) – Foremost(x) = ∀y. x 6= y → F(x, y) c.)Novice x is presently to the upupfit of novice y(y is to the left of x and there is no individual between them) -NextRight(x, y) = F(y, x) ∧ (∀z.z 6= x ∧ z 6= y → ¬(F(y, z) ∧ F(z, x))

    d.)Novice x is assist ( there is someindividual foremost, and x is presently to their upright) -∃y. F irst(y) ∧ NextRight(x, y)