Some students from a large class will be lined up left to right. There will be a

Question

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

Explanation / Answer

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

a.) Student x is in the line ( x is to the left of someone or someone is to the left of x ) - y.y 6= x (F(x, y) F(y,x)) b.)Student x is first in line (x is to the left of everyone (except themselves) ) - First(x) = y. x 6= y F(x, y) c.)Student x is immediately to the right of student y(y is to the left of x and there is no one between them) -NextRight(x, y) = F(y, x) (z.z 6= x z 6= y ¬(F(y, z) F(z, x))

d.)Student x is second ( there is someone first, and x is immediately to their right) -y. F irst(y) NextRight(x, y)

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