This document contains examples of quantified logic statements with predicates about animals living at a zoo, their relationships and properties. It also includes examples with predicates about dogs, their sizes and movie preferences. The examples are intended to illustrate the use of quantifiers like "every", "some", "there exists" to relate predicates with variables and connect them with logical operators like conjunction, negation and implication.

1. QL: Part 2

2. HW ANSWERS
Part A:
1. Amos, Bouncer and Cleo live at the Zoo.
Za&Zb&Zc
2. Bouncer is a reptile, but not an alligator.
Rb& ¬Ab
3. If Cleo loves Bouncer, then Bouncer is a monkey.
Lcb →Mb
4. If both Bouncer and Cleo are alligators, then Amos loves them both.
(Ab&Ac) → (Lab&Lac)
5. Some reptile lives at the zoo.
∃x (Rx&Zx)

3. Part 1: CONTINUATION
 6. Every alligator is a reptile.
∀x (Ax → Rx)
7. Every animal that lives at the zoo is either a monkey or an alligator.
∀x (Zx→(Mx v Ax))
8. There are reptiles which are not alligators.
∃x (Rx & ¬Ax)
9. Cleo loves a reptile.
∃x (Rx & Lcx)

4.  10. Bouncer loves all monkeys that live at the zoo.
- We have two space predicate: between a name and “all monkeys”
- Since we are talking about “all” animals which have property of being “a
monkey” we will need a quantifier
∀x [(Mx&Zx) →Lbx]

5. PART C
 1. Bertie is a dog who likes Samurai movies.
Bertie is a dog and Bertie likes to watch Samurai movies.
Db & Sb
2. Bertie, Emerson and Fergis are all dogs.
Berie is a dog, Emerson is a dog and Fergis is a dog.
Db & De & Df
3. Emerson is larger than Bertie, and Fergis is larger than Emerson.
Leb & Lfe
4. All dogs like samurai movies.
∀x (Dx →Sx)

6.  5. Only dogs like samurai movies.
∀x (Sx → Dx)
Doesn’t say that all dogs like samurai movies (which means that to be a dog
would be sufficient condition for liking samurai movies)
 Rather it says, that it is necessary that everyone who like samurai movies
are dogs.
∀x (¬ Dx → ¬ Sx)

7. 6. There is a dog that is larger than Emerson.
∃x (Dx & Lxe)
7. If there is a dog larger than Fergis, then there is a dog larger than Emerson.
∃x (Dx & Lf) → ∃x (Dx & Le)

8. TEAM WORK
PART A of exercise sheet
1. Sue is easygoing
Es
2. Michael is taller than Sue and Sue is taller than Henry.
Tms & Tsh
3. Sue likes Henry and Michael likes Rita.
Lsh & Lmr
4. If Rita likes Henry, then Rita is taller than Henry.
Lrh → Trh
5. If Michael is easygoing, then Rita is not easygoing.
Em → ¬ Er

9.  6. Henry likes Rita but Rita doesn’t like Henry.
Lhr & ¬ Lrh
7. Rita is taller than Henry and Rita is not taller than Sue.
Trh & ¬Trs

10. PART 2
 1. Everyone is easygoing.
∀xEx
2. No one likes Michael.
¬ ∃xLxm, ∀x ¬ Lxm
3. Michael likes everyone.
∀xLmx
4. Michael doesn’t like anyone.
There is no person that Michael likes.
¬ ∃xLmx, ∀x ¬ Lmx
5. Michael doesn’t like everyone.
It’s not the case that Michael likes all people (in his office).
¬∀xLmx

11.  6. Someone likes Sue.
There is a person (at least one) who likes Sue.
∃x Lxs
7. No one is taller than herself or himself.
¬ ∃xTxx,
∀x ¬ Txx