Exercises 1. Every set S can be(totally) ordered.(Hint: Use proposition to represent partial order and dichotomy, then try to apply compactness theorem. 2.Ex7/p46 3. Translate the following into predicates (a) Neither a or b is a member of every set (b) If horse are animals, then heads of horse are heads of animals (c) If some trains are late then all trains are late (d)There is no set of which every set is a member 4. Assume that we have a language with the following parameters: N, intended to mean "is a number"; 1, intended to mean"is interesting; < intended to mean"is less than". Give (vx)(N(x)→(I(x)→-(vy)(N(y)→((y)→-(x<y)) Translate them back to english 5. Ex 2(c, e, f)/ page 88 6. Ex 3/ page 88Exercises 1. Every set S can be (totally) ordered. (Hint: Use proposition to represent partial order and dichotomy, then try to apply compactness theorem.) 2. Ex 7/p46. 3. Translate the following into predicates (a) Neither a or b is a member of every set. (b) If horse are animals, then heads of horse are heads of animals. (c) If some trains are late then all trains are late. (d) There is no set of which every set is a member. 4. Assume that we have a language with the following parameters: N, intended to mean “is a number”; I, intended to mean “is interesting”; <, intended to mean “is less than”. Give (∀x)(N(x) → (I(x) → ¬(∀y)(N(y) → (I(y) → ¬(x < y))))). Translate them back to English. 5. Ex 2(c, e, f)/ page 88 6. Ex 3/ page 88 5