# 逻辑学考试代考 4AANA003 Elementary Logic

## MOCK PAPER

This is a mock paper for 4AANA003 Elementary Logic. It gives you an idea of the format, length and style of questions on the exam and you can use it for practice. The questions are taken from the Book of Problems—you can find answers to most in the latter’s solutions.
Warning. Do not assume that the exam will have the same question types or the same balance of topics.
MOCK EXAM PAPER
4AANA003 ELEMENTARY LOGIC
Semester 1 2021/22
TIME ALLOWED: ONLINE SUBMISSION WINDOW (within 24h of paper
release)
ANSWER ALL QUESTIONS (WITH NO FORMAL WORD LIMIT).

### 1. Answer the two questions below [15 points]  逻辑学考试代考

(a) Consider the relation R: {h1, 1i,h1, 2i,h2, 2i}. Say whether R is reflexive, symmetric, transitive, asymmetric, antisymmetric over the set {1, 2}. Briefly justify your answers.
(b) Consider the language L−1, a language of propositional logic containing only ¬, ∨ as connectives. Show, by constructing an appropriate truth table, than in L−1 we can express the connective ↑ whose truth table is:
φ ψ φ ↑ ψ
T T F
T F T
F T T
F F T

### 2. Using the method of full or partial truth tables, say whether the following sentences of L1 are tautologies or not. If not, give a counterexample. [10 points]

(a) P, Q |= P ∧ (¬P ∨ Q)
(b) P → R, Q → R |= P ∧ Q → R

### 3. Formalize the following arguments in L1. Provide a dictionary and make your formalization as detailed as possible. If you find an ambiguity in the argument, explain it to justify your choice of formalization.  逻辑学考试代考

Once formalized, say whether the argument is valid inpropositional logic by employing the method of full or partial tables. [15 points]
(a) Either we are deceived by an evil demon, or our belief-forming processes are reliable. If we are deceived by an evil demon, we will not have true beliefs. By contrasts, we will have true beliefs if our belief-formingprocess is reliable. Thus, we are not deceived by an evil demon.

(b) If Claudia finds Jonas and Jonas finds Martha, the knot is untied. Thus, if the knot is not untied, then Jonas does not find Martha or Claudia does not find Jonas.

### 4. Establish the following claims of L1 by employing natural deduction proofs. [15 points]

(a) `(P ∧ Q) ∨ P → P(b)` (P → Q) → (¬Q → ¬P)
(c) ¬(P ∧ Q) `¬P ∨ ¬Q<h3>5. Formalize the following sentences in L2 (the language of predicate logic) or L= (the language of predicate logic with identity) as appropriate. Provide a dictionary and make your formalization as detailed as possible. If you find an ambiguity, explain it to justify your choice of formalization. [15 points]  <a href="https://paperdaixie.com/%e9%80%bb%e8%be%91%e5%ad%a6%e8%80%83%e8%af%95%e4%bb%a3%e8%80%83/">逻辑学考试代考</a></h3>(a) There is a possible world that is accessible from the actual world.(b) A sentence is necessary in the actual world if and only if it is true in all possible worlds that are accessible from it.(c) Every natural number has a unique successor.<h3>6. Formalize the following arguments in L2. Provide a dictionary and make your formalization as detailed as possible. If you find an ambiguity, explain it to justify your choice of formalization.</h3>Once formalized, say whether the argument is valid in predicate logic. If it is, provide a natural deduction proof. If it is not, provide a counterexample to it. [20 points](a) Every instant of time is preceded by another instant.Therefore there is a first instant of time.<h3>(b) Nothing travels faster than light. Tachyons, which exist, travel faster than light. Therefore the universe has no beginning.  <a href="https://paperdaixie.com/%e9%80%bb%e8%be%91%e5%ad%a6%e8%80%83%e8%af%95%e4%bb%a3%e8%80%83/">逻辑学考试代考</a></h3>7. Establish the following claims of L2 by means of natural deduction proofs. [10 points](a) ∀x(Gx → P x), ¬P a` ∃yQy
(b) ∀x∀y∀z(Rxy ∧ Ryz → Rxz) ` ¬∃u∀x(Rux ∧ Rxu ∧ ¬Ruu)