Exam (elaborations)
COS3761 EXAM PACK 2024
- Institution
- University Of South Africa (Unisa)
Recent exam questions and answers and summarized notes for exam preparation. for assistance. All the best on your exams!!
[Show more]
Content preview
COS3761EXAM PACK
,UNIVERSITY EXAMINATIONS
JUNE/JULY 2021
COS3761
Formal Logic III
Welcome to the COS3761 exam.
NB you can only download your paper from the myExams site!
To proceed with the writing of the examination, click on the link below:
https://myexams.unisa.ac.za/portal/login
Instructions:
Examination is for 100 marks. Duration of exam is 2 hours
Answer all questions.
The paper consists of 7 pages
Do all rough work in the answer book
Number your answers and label your rough work clearly
The mark for every question appears in brackets next to the question
Student should do the Honesty Declaration.
Follow the UNISA instructions for uploading your script
EXAMINATION PANEL:
First examiner: S Vallabhapurapu
Second examiner: Mr K Halland
External examiner: Dr C Dongmo
ALL THE BEST!
[TURN OVER]
, 2
COS3761
June/July 2021
QUESTION 1 [25]
Question 1.1
Consider the following propositional symbols and their intended meanings:
p : The earth is round
q: The Moon is cold
r: A lunar eclipse occurs when the
earth comes in between the sun
and the moon
(i) Express the following declarative sentence in propositional logic using the propositional symbols
as given above:
Either the earth is round or the moon is not cold (2)
(ii) Express the following propositional logic formula in English where the propositional symbols
have the meanings given above:
p (q ∨ r) (2)
Question 1.2
Use the basic natural deduction rules for propositional logic to prove the validity of the following
sequents:
(i) p → q├ ¬ p ∨ q (6)
(ii) ¬ p ∨ q├ ¬ (¬ p q) (6)
Question 1.3
Show that the following sequent is not valid by giving an appropriate valuation. (4)
p q, q ( p r) , r├ p
Explain why your valuation proves that the sequent is not valid.
[TURN OVER]
, 3
COS3761
June/July 2021
Question 1.4
Use the HORN algorithm to prove that the following Horn formula is satisfiable or not satisfiable.
Show each step.
(q r s) (q r T) (s q ) (q s r) (5)
QUESTION 2 [37]
Question 2.1
Consider the following predicate and constant symbols and their intended meanings:
S(x): x is a student in this class
C(x): x has visited Canada
E(x): x has visited Europe
(i) Express the following predicate logic formula in English, where the symbols have the meanings
as given above:
x[S(x) (C(x)∨E(x))] (3)
(ii) Express the following declarative sentence in predicate logic using the symbols as given above:
Some student in this class has visited Canada (3)
Question 2.2
Let
P be a predicate symbol with one argument and Q a predicate with two arguments, respectively
a is a constant
x, y are variables
State which of the following are well formed formulas:
(i) ∀x P(x) (1)
(ii) x Q(x, y) (1)
[TURN OVER]
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller iStudy. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R50,00. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
85443 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy summaries for 14 years now