Show transcribed image text Question 4. Some students from a large class like ours are lined up left to right. You may assume at least two students are in the line. Translate each of the following assertions into predicate formulas with the set of students in the class as the universe of discourse. The only predicates you may use are: ? equality between students, written x = y, and ? F(x, y), defined to mean student x is somewhere to the left of student y in line. For example, in the line CDA, both F(C, A) and F(C, D) are true. On the contrary. F(D,C). F(B, A), and F(B, B)are all false. Once you define a formula for a predicate below, you can and should use that predicate in further formulas. We'll start you off with this definition of 1NLINE(x) : 3y.(F(x,y) V F(y. x)) (which you can now use). This predicate says x is in the line if and only if there is some person y who is either to the left or to the right of x in line. (a) LEFTMOST(x): Student x is leftmost in line. (b) SUCCESSOR( x, y): Student x is immediately to the right of student yin line. (c) SECOND(x): Students is second from the left in line. (d) MIDDLE(x): Student .r is in the middle (i.e., not at either end) of the line.