Solutions to Quiz One


Note that some problems might have more than one correct answer:
1.
(a) ___ is shorter than ___   Arity: 2   Names: Taft Hall, University Hall
(b) ___ is larger than ___   Arity: 2   Names: Lake Michigan, Lake Ontario
(c) ___ and ___ combined are larger than ___ Arity: 3   Names: Lake Michigan, Lake Ontario, Lake Superior

2.
(a)
(b)
| Almost all dogs prefer Bone-O
| All corgis are dogs
| All corgis prefer Bone-O              invalid		 | a is to the left of b
| a is to the left of c
| b is to the left of c              invalid

3.
(a) F
 (b) T
 (c) T
 (d) T
 (e) F
(f) T
 (g) F
 (h) Not evaluable
 (i) It's false
 (j) It's true

4.
(a) Valid – it is sound in A
(b) Invalid – A is a counter-example
(c) Can't tell
(d) They're all true
(e) It's invalid

5.
(a) SYM, REF
(b) TRAN
(c) none
(d) ≤
(e) is an ancestor of

6.
(a) George H bush was President for less time than Ronald Reagan
(b) ¬Larger(a,c) ^ ¬Smaller(a,c)
(c) a is either not small or not a tetrahedron
(d) ¬(Small(a) v Tet(a))

7.
(a) a is larger than b, so since b is d, a is larger than d by II. But d is larger than e, so a is larger than e by transitivity (of larger than). So e is smaller than a because larger than and smaller than are inverses.
(b)
| 1. Larger(a,b)
| 2. Larger(d,e)
| 3. b=d
| 4. Larger(a,d)      =Elim 1,3
| 5. Larger(a,e)      AnaCon 2,4
| 6. Smaller(e,a)    AnaCon 5

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