COS3761 assignment 2 solutions 2023

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Formal Logic III
COS3761

2023

Assignment 2

School of Computing

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ASSIGNMENT 2
Please note that this is a written assignment. You need to prepare and submit a
document in Word or PDF format.



Predicates
D(x) x is a degree
M(x, y) x is a major
subject of y
L(x, y) x loves y
H(x, y) x hates y
T(x, y) x takes y
Constants
c Computer
Science
i Information
Systems

QUESTION 1
Use the predicate, and constant symbols and their intended meanings given in Table 2 to
translate the English sentences given below into predicate logic:


Question 1.1:
"There is a degree with Information Systems as a major subject."
Translation: ∃x(D(x) ∧ M(i, x))


Question 1.2:
"Everyone who loves Computer Science takes it as a major subject of a degree."
∀x((L(x, c) ∧ D(y) ∧ M(c, y)) → T(x, y))


Question 1.3:
"If someone loves Computer Science, they do not necessarily hate Information
Systems."
Translation: ∀x((L(x, c) → ¬H(x, i)))


Question 1.4:
"Some students take Information Systems or Computer Science, but not both."
∃x(D(x) ∧ ((M(i, x) ∧ ¬M(c, x)) ∨ (¬M(i, x) ∧ M(c, x))))