UNIVERSITY EXAMINATIONS
OCTOBER/NOVEMBER 2024
COS3761
Formal Logic III
100 Marks
2 HOURS 15 MINUTES
Instructions:
Examination is for 100 marks. Answer all questions.
IRIS tool is used for the exam
The paper consists of 6 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: Prof S Vallabhapurapu
Second examiner: Mr K Halland
External Examiner : Prof C Tu
ALL THE BEST!
[TURN OVER]
, 2
COS3761
OCT/NOV2024
QUESTION 1 [25]
Question 1.1
Consider the following propositional symbols and their intended meanings:
p : It is raining
q: The sprinklers are on
r: The grass is wet
(i) Express the following declarative sentence in propositional logic using the propositional symbols
as given above:
If the grass is wet, then either it is raining or the sprinklers are on. (2)
(ii) Express the following propositional logic formula in English where the propositional symbols
have the meanings given above:
¬ (p → r) ∨ (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 r) → (q r) ) (8)
(ii) ├ ¬ (p ¬ p) (5)
Question 1.3
Show that the following sequent is not valid by giving an appropriate valuation.
p → q ⊢ (p ∧ q) → r
Explain why your valuation proves that the sequent is not valid. (3)
[TURN OVER]
OCTOBER/NOVEMBER 2024
COS3761
Formal Logic III
100 Marks
2 HOURS 15 MINUTES
Instructions:
Examination is for 100 marks. Answer all questions.
IRIS tool is used for the exam
The paper consists of 6 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: Prof S Vallabhapurapu
Second examiner: Mr K Halland
External Examiner : Prof C Tu
ALL THE BEST!
[TURN OVER]
, 2
COS3761
OCT/NOV2024
QUESTION 1 [25]
Question 1.1
Consider the following propositional symbols and their intended meanings:
p : It is raining
q: The sprinklers are on
r: The grass is wet
(i) Express the following declarative sentence in propositional logic using the propositional symbols
as given above:
If the grass is wet, then either it is raining or the sprinklers are on. (2)
(ii) Express the following propositional logic formula in English where the propositional symbols
have the meanings given above:
¬ (p → r) ∨ (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 r) → (q r) ) (8)
(ii) ├ ¬ (p ¬ p) (5)
Question 1.3
Show that the following sequent is not valid by giving an appropriate valuation.
p → q ⊢ (p ∧ q) → r
Explain why your valuation proves that the sequent is not valid. (3)
[TURN OVER]
