COS3761 OCT/NOV 2024 Exam paper

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!




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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)

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