lab 1 and key

quiz 1 and key

Grading rubric:

• Page 1
  • have keys and expressions
  • correct logical syntax
  • q1 is prep → do well
  • q2 is fight ∧ look
  • q3 is (perf ∨ staff) → (early ⊕ on-time)
  • q4 contains (midget ∨ giant) → (size ∧ shop)
  • q4 contains ∧ never-met
• Page 2 (50%)
  • have keys and expressions
  • correct logical syntax
  • q1 is prep → do well
  • q2 is fight ∧ look
  • q3 is (perf ∨ staff) → (early ⊕ on-time)
  • q4 contains (midget ∨ giant) → (size ∧ shop)
  • q4 contains ∧ never-met

lab 2 and key

quiz 2 and key

Grading rubric:

• correct logic syntax
• q1 is simple English
• q1 means like iff questing
• q2 has key
• q2 means ¬(hurt ∨ tired) → win
• q3 shows non-equivalence
• q3 either a counter-example or a derivation
• q4 goes from one to other
• q4 labels rules
• q4 applies rules correctly

lab 3 and key

quiz 3 and key

Grading rubric:

• Page 1
  • q1 something as ∃ x . F(x)
  • q1 and q3 nothing as ∄ x . G(x)
  • q2 some as ∃x . P(x) ∧ Q(x)
  • q2 and q3 all as ∀x . Q(x) → R(x)
  • q3 no as ∄x . Q(x) ∧ P(x)
• Page 2
  • q4 ∄x . M(x) ∧ A(x)
  • q5 ∀x . […] → L(s,x)
  • q5 both A(x) and L(x,h) in antecedent
  • q6 ∀x . ∃y .
  • q6 z(x) → (L(x,y) ∧ L(y,x))

lab 4 and key

quiz 4 and key

Grading rubric:

• Page 1
  • q1 has symbol key, including known by and me
  • q1 ∃ person ∀ people, people knows person
  • q1 … and person knows me
  • q2 expressed in prose
  • q2 roughly follows outline
• Page 2
  • q3 same expression on every underlined blank
  • q4 valid logic
  • q5 valid logic
  • q4 and q5 expressed in prose

lab 5 and key

quiz 5 and key

Grading rubric:

• q1 is {{}, {3}, {4}, {3, 4}}
• q2 is {1, 2, 3, 4, 5} with no duplicates
• q3 is {2}
• q4 has all of A and none of B (i.e., {1, 4})
• q5 is {{}, {3}}
• q6 is a set of natural numbers = {1,2}
• q7 is a subset of B = {2}
• q8 is a set of sets = {{2,4}, {3,4}}
• q9-11 is 3, 8, 16
• q12-14 is ⊥, ⊤, ⊥

lab 6 and key

quiz 6 and key

Grading rubric:

• Page 1
  • base case is f(0) = 0
  • inductive step assumption is f(x-1) = (x-1)(x)
  • inductive step follows outline
  • written in prose
  • labels cases and principle of induction
• Page 2
  • base case is f(0) terminates
  • inductive step makes assumption
  • inductive step appeals to f(x-1) termination
  • no logical errors
  • readable (prose and/or symbolic math)

lab 7 and key

quiz 7 and key

Grading rubric:

• Page 1
  • q1 quantifiers (some rabbits that all (yellow) snakes)
  • q1 logic (yellow snakes don’t eat)
  • 18 = 2×3×3
  • 81 = 3×3×3×3
  • 2^20 × 3^40
  • {1, 3, 7, 9}
• Page 2
  • assume 7/3 is integer
  • algebra to get contradiction
  • .. which means assumption wrong
  • no logical errors
  • readable (prose and/or symbolic math)

lab 8 and key

quiz 8 and key

There is no rubric because the quiz version printed and shown in class contained an error large enough that the quiz was dropped entirely.

lab 9 and key

quiz 9 and key

Grading rubric:

• Page 1
  • q1 2^10
  • q2 10 choose 6
  • q3 26 * 36^5
  • q4 6/6^3
  • q5 6!/2! - 1
• Page 2
  • base case includes n=0
  • base case logic right
  • inductive step assumes at some n
  • algebra correct
  • proof correct

lab 10 and key

quiz 10 and key

Grading rubric:

• q1 ∃t
• q1 addresses conservativeness and completeness
• q2 ∄t∀p or ∀t¬∀p or ∀t∃p
• q2 perfect as B(p)↔︎B(p,t) or equivalent
• q3 every test handles some program
• q4 some test handles every program
• q5 example is ℚ→ℚ and total
• q5 example is injective and not surjective
• q6 example is ℚ→ℕ and total
• q6 example is surjective

lab 11 and key

There was no quiz due to failure of the quizzing site computer system.

Not yet released