COS3761 Assignment 2 Solutions/Answers 2025

COS3761 ASSIGNMENT 2

QUESTION 1

1.1

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

We translate this as:
C(c) ∧ ∀x (M(c, x) ∧ ¬(P(s, c) ∨ M(c, a)) → ¬W(c))

Explanation: For all matches played by Cavaliers (club c), if Sam does not play for them
and they are not playing against Aviators, then they do not win.




1.2

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

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

Explanation: Every teenager is either a football or rugby player but not both.




1.3

"When Aviators play against any club they win only if at least one player's brother also
plays for Aviators."

∀x ((C(x) ∧ M(a, x)) → (W(a) → ∃y (P(y, a) ∧ P(b(y), a))))

Explanation: For any club x, if Aviators play against them and Aviators win, then there is
some player whose brother also plays for Aviators.