Chapter 1 - Section 1.4 - Predicates and Quantifiers - Exercises - Page 55: 37

In each case we need to make up predicates. The answers are certainly not unique and depend on the choice of predicate, among other things. a) I::!x((F(x, 25000) V S(x, 25)) --* E(x)), where E(x) is "Person x qualifies as an elite flyer in a given year," F(x, y) is "Person x flies more than y miles in a given year," and S(x, y) is "Person x takes more than y flights in a given year" b) I::!x(((M(x)I\T(x, 3))V(,M(x)I\T(x, 3.5))) --* Q(x)), where Q(x) is "Person x qualifies for the marathon," l'vl(x) is "Person x is a man," and T(x, y) is "Person x has run the marathon in less than y hours" c) M --* ((H(60) V (H(45) 1\ T)) 1\ l::!yG(B,y)) , where M is the proposition "The student received a masters degree," H(x) is "The student took at least x course hours," T is the proposition "The student wrote a thesis," and G(x, y) is "The person got grade x or higher in his course y" d) 3x ((T(x, 21) 1\ G(x, 4.0)), where T(x, y) is "Person x took more than y credit hours" and G(x,p) is "Person x earned grade point average p" (we assume that we are talking about one given semester)

In each case we need to make up predicates. The answers are certainly not unique and depend on the choice of predicate, among other things. a) I::!x((F(x, 25000) V S(x, 25)) --* E(x)), where E(x) is "Person x qualifies as an elite flyer in a given year," F(x, y) is "Person x flies more than y miles in a given year," and S(x, y) is "Person x takes more than y flights in a given year" b) I::!x(((M(x)I\T(x, 3))V(,M(x)I\T(x, 3.5))) --* Q(x)), where Q(x) is "Person x qualifies for the marathon," l'vl(x) is "Person x is a man," and T(x, y) is "Person x has run the marathon in less than y hours" c) M --* ((H(60) V (H(45) 1\ T)) 1\ l::!yG(B,y)) , where M is the proposition "The student received a masters degree," H(x) is "The student took at least x course hours," T is the proposition "The student wrote a thesis," and G(x, y) is "The person got grade x or higher in his course y" d) 3x ((T(x, 21) 1\ G(x, 4.0)), where T(x, y) is "Person x took more than y credit hours" and G(x,p) is "Person x earned grade point average p" (we assume that we are talking about one given semester)