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COS3761 Assignment 3(QUIZ) 2023 - suggested answers
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COS3761Assignment 3
2023
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ASSIGNMENT 3
Please note: This is an MCQ assignment – called a Quiz on myUnisa. There are 20 questions in this
assignment, each counting 5 marks. For each question, choose one out of the four options.
Unisa Guides
, x2
x₁
p p, q x₃
q
x₄
Figure 1: Kripke model used in Questions 1 to 5 QUESTION
In which world of the Kripke model in Figure 1 is the formula ◊ p ∧ □ q true?
Option 1: world x₁
Option 2: world x₂
Option 3: world x₃ ✅
Option 4: world x4
• The formula ◊ p means that there is a possibility of ‘p’ being true in the current world or
some accessible world. In world x3, ‘p’ is true.
• The formula □ q means that ‘q’ is true in the current world and all its accessible worlds.
In world x3, ‘q’ is true and it’s also true in its accessible world (x4).
QUESTION 2
Which of the following does not hold in the Kripke model in Figure 1?
Option 1: x₁ ◊◊p
Option 2: x₂ □p✅
Option 3: x₃ □p∧□q
Option 4: x₄ □□ p
• The formula □ p means that ‘p’ is true in the current world and all its accessible worlds. In
world x2, ‘p’ is not labelled, which means ‘p’ is not true in this world. Therefore, □ p does not
hold in world x2.
, QUESTION 3
Which of the following holds in the Kripke model given in Figure 1?
Option 1: x₁ □p
Option 2: x₂ ◊ (p → q)
Option 3: x₃ ◊p∨□¬q
Option 4: x₄ ◊ (p ∨ q) ✅
The formula ◊ (p ∨ q) means that there is a possibility of either ‘p’ or ‘q’ being true in the current world
or some accessible world. In world x4, ‘q’ is true. Therefore, ◊ (p ∨ q) holds in world x4
QUESTION 4
Which of the following formulas are satisfied by the Kripke model given in Figure 1?
Option 1: ◊ p ✅
Option 2: □q
Option 3: □ (p ∨ q)
Option 4: ◊p∨q
This formula means that there is a possibility of ‘p’ being true in some world. In the Kripke model you
described, ‘p’ is true in worlds x1 and x3. Therefore, the formula ◊ p is satisfied by the Kripke model.
QUESTION 5
Which of the following formulas are not satisfied by the Kripke model given in Figure 1?
Option 1: □ p ∨ ◊ q
Option 2: □◊p ✅
Option 3: q∨◊¬q
Option 4: p∨□q
This formula means that ‘p’ is true in the current world or ‘q’ is true in all worlds. In the Kripke model
you described, ‘p’ is not true in all worlds (it’s not true in x2 and x4), and ‘q’ is also not true in all worlds
(it’s not true in x1 and x2). Therefore, this formula is not satisfied by the Kripke model.
QUESTION 6
If we interpret □ φ as "It ought to be that φ ", which of the following formulas correctly expresses the
English sentence
If it is permitted that politicians can break the law, then it ought not to be the case that we are
punished for breaking the law.
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