COS3761 Assignment 3 2025 ANSWERS

COS3761
ASSIGNMENT 3 2025

UNIQUE NO.
DUE DATE: 2025

, Formal Logic III

COS3761 Assignment 3 (2025)

QUESTION 1

In which world of the Kripke model in Figure 1 is the formula ◊p ∧ □q true?
Answer: Option 1: world x₁

QUESTION 2

Which of the following does not hold in the Kripke model in Figure 1?
Answer: Option 2: x₂ ⊭ □p

QUESTION 3

Which of the following holds in the Kripke model given in Figure 1?
Answer: Option 2: x₂ ⊨ ◊(p ∨ q)

QUESTION 4

Which of the following formulas is true in the Kripke model given in Figure 1?
Answer: Option 3: □◊q

QUESTION 5

Which of the following formulas is false in the Kripke model given in Figure 1?
Answer: Option 2: □◊p

QUESTION 6

It ought to be the case that if it rains outside then it is permitted to take leave
from work.
Let p = "It rains outside", q = "take leave from work"
Answer: Option 1: □(p → ¬□¬q)