COS3761 Assignment 2 (Comprehensive Response) Due July 2025

COS3761
Assignment 2
Due July 2025

, COS3761
Assignment 2
Due July 2025




Question 1 [18 marks]

Translate the following English sentences into predicate logic using the given symbols.

1.1 (3 marks)

Cavaliers do not win any match except when Sam plays for them or when they play against
Aviators.

Solution:

Symbols:

• W(x): x wins

• P(s, c): Sam plays for Cavaliers

• M(c, x): Cavaliers play against x

• a: Aviators

Translation: ¬W(c) → (P(s, c) ∨ ∃x (M(c, x) ∧ x = a))

Explanation: "Except when" indicates a conditional situation: Cavaliers can only win if
either Sam plays for them or they play against Aviators. This is best represented using
implication.

, 1.2 (3 marks)

Every teenager is a football or a rugby player but no teenager plays both.

Solution:

Symbols:

• T(x): x is a teenager

• F(x): x is a football player

• R(x): x is a rugby player

Translation: ∀x (T(x) → ((F(x) ∨ R(x)) ∧ ¬(F(x) ∧ R(x))))

Explanation: First part ensures every teenager plays at least one sport; second part ensures
mutual exclusivity.



1.3 (2 marks)

Aviators.

Solution:

Symbol:

• C(a): Aviators are a club

Translation: C(a)

Explanation: Simple assertion that Aviators are a club.