COS3761/103/0/2023
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.
x2
x₁
p p, q x₃
q
x₄
Figure 1: Kripke model used in Questions 1 to 5
QUESTION 1
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
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
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)
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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.
x2
x₁
p p, q x₃
q
x₄
Figure 1: Kripke model used in Questions 1 to 5
QUESTION 1
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
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
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)
17
