COS3761
ASSIGNMENT 3 2025
UNIQUE NO.
DUE DATE: 2025
, lOMoARcPSD|21997160
COS3761/103/2025
ASSIGNMENT 3
qq x₂
q
p x₃
p, q
x₁
q
x₄
Figure 1: Kripke model used in Questions 1, 2, 3, 4 and 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: Option 1 and Option 3 are true.
UESTION 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
19
ASSIGNMENT 3 2025
UNIQUE NO.
DUE DATE: 2025
, lOMoARcPSD|21997160
COS3761/103/2025
ASSIGNMENT 3
qq x₂
q
p x₃
p, q
x₁
q
x₄
Figure 1: Kripke model used in Questions 1, 2, 3, 4 and 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: Option 1 and Option 3 are true.
UESTION 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
19
